Pub Date : 2023-10-13DOI: 10.1080/01630563.2023.2265649
Fuad Kittaneh, Hamid Reza Moradi, Mohammad Sababheh
AbstractExtending certain scalar and norm inequalities, we present new inequalities for the numerical radius, which generalize and refine some known results. Applications of the obtained inequalities include a new original proof of the matrix arithmetic-geometric mean inequality and certain extensions of some well-established results from the literature for products of matrices.KEYWORDS: Convex functionnorm inequalitynumerical radiusMATHEMATICS SUBJECT CLASSIFICATION: Primary: 15A60Secondary: 47A1247A30 Authors’ contributionsThe authors have contributed equally to this work.Disclosure statementAll authors declare that they have no conflicts of interest.Additional informationFundingThe authors did not receive any funding to accomplish this work.
{"title":"Mean Inequalities for the Numerical Radius","authors":"Fuad Kittaneh, Hamid Reza Moradi, Mohammad Sababheh","doi":"10.1080/01630563.2023.2265649","DOIUrl":"https://doi.org/10.1080/01630563.2023.2265649","url":null,"abstract":"AbstractExtending certain scalar and norm inequalities, we present new inequalities for the numerical radius, which generalize and refine some known results. Applications of the obtained inequalities include a new original proof of the matrix arithmetic-geometric mean inequality and certain extensions of some well-established results from the literature for products of matrices.KEYWORDS: Convex functionnorm inequalitynumerical radiusMATHEMATICS SUBJECT CLASSIFICATION: Primary: 15A60Secondary: 47A1247A30 Authors’ contributionsThe authors have contributed equally to this work.Disclosure statementAll authors declare that they have no conflicts of interest.Additional informationFundingThe authors did not receive any funding to accomplish this work.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135858351","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-12DOI: 10.1080/01630563.2023.2265722
D. Kumar, A. K. B. Chand, P. R. Massopust
AbstractA novel approach to zipper fractal interpolation theory for functions of several variables is presented. Multivariate zipper fractal functions are constructed and then perturbed through free choices of base functions, scaling functions, and a binary matrix called signature to obtain their zipper α-fractal versions. In particular, we propose a multivariate Bernstein zipper fractal function and study its coordinate-wise monotonicity which depends on the values of signature. We derive bounds for the graph of a multivariate zipper fractal function by imposing conditions on the scaling factors and the Hölder exponent of the associated germ function and base function. The box dimension result for multivariate Bernstein zipper fractal function is derived. Finally, we study some constrained approximation properties for multivariate zipper Bernstein fractal functions.KEYWORDS: Box dimensionfractal interpolation functionmonotonicitymultivariate Bernstein operatorpositivityzipperMATHEMATICS SUBJECT CLASSIFICATION: 28A8041A6341A0541A2941A3065D05 AcknowledgmentThe authors are thankful to the annonymous reviewers for their constructive suggestions to improve the presentation of the paper.
{"title":"Multivariate Zipper Fractal Functions","authors":"D. Kumar, A. K. B. Chand, P. R. Massopust","doi":"10.1080/01630563.2023.2265722","DOIUrl":"https://doi.org/10.1080/01630563.2023.2265722","url":null,"abstract":"AbstractA novel approach to zipper fractal interpolation theory for functions of several variables is presented. Multivariate zipper fractal functions are constructed and then perturbed through free choices of base functions, scaling functions, and a binary matrix called signature to obtain their zipper α-fractal versions. In particular, we propose a multivariate Bernstein zipper fractal function and study its coordinate-wise monotonicity which depends on the values of signature. We derive bounds for the graph of a multivariate zipper fractal function by imposing conditions on the scaling factors and the Hölder exponent of the associated germ function and base function. The box dimension result for multivariate Bernstein zipper fractal function is derived. Finally, we study some constrained approximation properties for multivariate zipper Bernstein fractal functions.KEYWORDS: Box dimensionfractal interpolation functionmonotonicitymultivariate Bernstein operatorpositivityzipperMATHEMATICS SUBJECT CLASSIFICATION: 28A8041A6341A0541A2941A3065D05 AcknowledgmentThe authors are thankful to the annonymous reviewers for their constructive suggestions to improve the presentation of the paper.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135969932","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-10DOI: 10.1080/01630563.2023.2263977
Neha Kajla, Naokant Deo
AbstractAs part of this study, we propose a modification of the so-known Lupaş-Kantrovich that preserve exponential function e−x. To support this claim, we estimate the convergence rate of the operators in terms of both the usual and exponential modulus of continuity. Our analysis also includes a global estimate and quantitative Voronovskaya results. Demonstrating the effectiveness of modified operators, we provided a result and supporting graphs.KEYWORDS: Exponential functionsrate of convergenceVoronovoskaya theoremMATHEMATICS SUBJECT CLASSIFICATION: 41A2541A36 Disclosure statementThis work has no conflicts of interest.Additional informationFundingCSIR is funding this research with Reference No:08/133(0021)/2018-EMR-1 for the first author.
{"title":"An approach to preserve functions with exponential growth by using modified Lupaş-Kantrovich operators","authors":"Neha Kajla, Naokant Deo","doi":"10.1080/01630563.2023.2263977","DOIUrl":"https://doi.org/10.1080/01630563.2023.2263977","url":null,"abstract":"AbstractAs part of this study, we propose a modification of the so-known Lupaş-Kantrovich that preserve exponential function e−x. To support this claim, we estimate the convergence rate of the operators in terms of both the usual and exponential modulus of continuity. Our analysis also includes a global estimate and quantitative Voronovskaya results. Demonstrating the effectiveness of modified operators, we provided a result and supporting graphs.KEYWORDS: Exponential functionsrate of convergenceVoronovoskaya theoremMATHEMATICS SUBJECT CLASSIFICATION: 41A2541A36 Disclosure statementThis work has no conflicts of interest.Additional informationFundingCSIR is funding this research with Reference No:08/133(0021)/2018-EMR-1 for the first author.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136295097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-09DOI: 10.1080/01630563.2023.2266004
Rohit Patel, V. Vijayakumar, Shimpi Singh Jadon, Anurag Shukla
AbstractIn this article, the main objective is the conversation about the optimal control problem of the semilinear thermoelastic system, in which the control term is placed solely in the thermal equation. We discuss the existence and uniqueness of mild solutions by applying the contraction mapping for the considered system. By assuming some conditions specified Lagrange’s problem acknowledges at least one optimal control pair. For proving the main results, we are assuming the Lipschitz condition on the nonlinear term.KEYWORDS: Existencemild solutionoptimal controlsemilinear thermoelastic systemuniquenessMATHEMATICS SUBJECT CLASSIFICATION: 34A0834K3549J15
{"title":"An Analysis on the Existence of Mild Solution and Optimal Control for Semilinear Thermoelastic System","authors":"Rohit Patel, V. Vijayakumar, Shimpi Singh Jadon, Anurag Shukla","doi":"10.1080/01630563.2023.2266004","DOIUrl":"https://doi.org/10.1080/01630563.2023.2266004","url":null,"abstract":"AbstractIn this article, the main objective is the conversation about the optimal control problem of the semilinear thermoelastic system, in which the control term is placed solely in the thermal equation. We discuss the existence and uniqueness of mild solutions by applying the contraction mapping for the considered system. By assuming some conditions specified Lagrange’s problem acknowledges at least one optimal control pair. For proving the main results, we are assuming the Lipschitz condition on the nonlinear term.KEYWORDS: Existencemild solutionoptimal controlsemilinear thermoelastic systemuniquenessMATHEMATICS SUBJECT CLASSIFICATION: 34A0834K3549J15","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135096011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-06DOI: 10.1080/01630563.2023.2262819
Palle E. T. Jorgensen, James F. Tian
AbstractWe study multiple notions of Hilbert spaces of functions which, via the respective inner products, reproduce function values, or differences of function values. We do this by extending results from the more familiar settings of reproducing kernel Hilbert spaces, RKHSs. Our main results deal with operations on infinite graphs G=(V,E) of vertices and edges, and associated Hilbert spaces. For electrical network models, the differences f(x)−f(y) represent voltage differences for pairs of vertices x, y. In these cases, relative RKHSs will depend on choices of conductance functions c, where an appropriate function c is specified as a positive function defined on the edge-set E from G. Our present study of higher order differences, using choices of relative RKHSs, is motivated in part by existing numerical algorithms for discretization of PDEs. Our approach to higher order differences uses both combinatorial operations on graphs, and operator theory for the respective RKHSs. Starting with a graph G=(V,E), we introduce an induced graph G′ such that the vertices in G′ are the edges in E from G, while the edges in G′ are pairs of neighboring edges from G.KEYWORDS: Conduction functionsdrop operatorgraph Laplacianhigher order differencesinduced graphsisometriesnetwork modelsrelative reproducingreproducing kernel Hilbert spaceresistance distanceMATHEMATICS SUBJECT CLASSIFICATION: Primary: 47B3247B9047N4047N70Secondary: 05C6305C9046C0546E2247B25 Data availability statementThe datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.Disclosure statementThe authors report there are no competing interests to declare.Additional informationFundingNo funding was received to assist with the preparation of this manuscript. The authors have no relevant financial or non-financial interests to disclose.
{"title":"Higher Order Difference Operators and Associated Relative Reproducing Kernel Hilbert Spaces","authors":"Palle E. T. Jorgensen, James F. Tian","doi":"10.1080/01630563.2023.2262819","DOIUrl":"https://doi.org/10.1080/01630563.2023.2262819","url":null,"abstract":"AbstractWe study multiple notions of Hilbert spaces of functions which, via the respective inner products, reproduce function values, or differences of function values. We do this by extending results from the more familiar settings of reproducing kernel Hilbert spaces, RKHSs. Our main results deal with operations on infinite graphs G=(V,E) of vertices and edges, and associated Hilbert spaces. For electrical network models, the differences f(x)−f(y) represent voltage differences for pairs of vertices x, y. In these cases, relative RKHSs will depend on choices of conductance functions c, where an appropriate function c is specified as a positive function defined on the edge-set E from G. Our present study of higher order differences, using choices of relative RKHSs, is motivated in part by existing numerical algorithms for discretization of PDEs. Our approach to higher order differences uses both combinatorial operations on graphs, and operator theory for the respective RKHSs. Starting with a graph G=(V,E), we introduce an induced graph G′ such that the vertices in G′ are the edges in E from G, while the edges in G′ are pairs of neighboring edges from G.KEYWORDS: Conduction functionsdrop operatorgraph Laplacianhigher order differencesinduced graphsisometriesnetwork modelsrelative reproducingreproducing kernel Hilbert spaceresistance distanceMATHEMATICS SUBJECT CLASSIFICATION: Primary: 47B3247B9047N4047N70Secondary: 05C6305C9046C0546E2247B25 Data availability statementThe datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.Disclosure statementThe authors report there are no competing interests to declare.Additional informationFundingNo funding was received to assist with the preparation of this manuscript. The authors have no relevant financial or non-financial interests to disclose.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135351225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-02DOI: 10.1080/01630563.2023.2261742
Yamin Sayyari, Mehdi Dehghanian
AbstractIn this paper, we introduce an universal definition (fgh-convex) that results in several types of convexity. Particular cases of the fgh-convex are for instance the harmonically convex, geometrically convex, GA-convex, log-convex, and several others. Also, we obtain some useful inequalities such as Jensen, generalization of Jensen Hermite-Hadamard, Mercer inequalities. Moreover, with the use of these inequalities, we obtained bounds for Shannon’s entropy and Kapur’s entropy. Finally, we found an application of the obtained inequalities in means.KEYWORDS: fgh-convex functionJensens inequalityKapur’s entropyShannon’s entropy2010 MATHEMATICS SUBJECT CLASSIFICATION: Primary: 26B2526D20 Disclosure statementThe authors declare that they have no competing interests.
{"title":"<i>fgh</i> -Convex Functions and Entropy Bounds","authors":"Yamin Sayyari, Mehdi Dehghanian","doi":"10.1080/01630563.2023.2261742","DOIUrl":"https://doi.org/10.1080/01630563.2023.2261742","url":null,"abstract":"AbstractIn this paper, we introduce an universal definition (fgh-convex) that results in several types of convexity. Particular cases of the fgh-convex are for instance the harmonically convex, geometrically convex, GA-convex, log-convex, and several others. Also, we obtain some useful inequalities such as Jensen, generalization of Jensen Hermite-Hadamard, Mercer inequalities. Moreover, with the use of these inequalities, we obtained bounds for Shannon’s entropy and Kapur’s entropy. Finally, we found an application of the obtained inequalities in means.KEYWORDS: fgh-convex functionJensens inequalityKapur’s entropyShannon’s entropy2010 MATHEMATICS SUBJECT CLASSIFICATION: Primary: 26B2526D20 Disclosure statementThe authors declare that they have no competing interests.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135828676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-27DOI: 10.1080/01630563.2023.2259697
Yan-Ling Fu, Wei Zhang, Yu Tian
AbstractH-S-frame is in essence a more general operator-valued frame than generalized frames. In this paper, we aim at studying the characterizations and representations of H-S-frames in H (Hilbert space). We first introduce the notion of H-S-preframe operator, and characterize the H-S-frames, Parseval H-S-frames, H-S-Riesz bases, H-S-orthonormal bases and dual H-S-frames with the help of H-S-preframe operators, and obtain the accurate expressions of all dual H-S-frames of a given H-S-frame by drawing support from H-S-preframe operators. Then we discuss the sum of H-S-frames through the properties of H-S-preframe operators. Finally, with the help of the approaches and skills of frame theory, we present the representations of H-S-frames and H-S-Bessel sequences. Specifically, the necessary and sufficient condition for the H-S-frame to be represented as a combination of two H-S-orthonormal bases is that the H-S-frame is an H-S-Riesz basis.KEYWORDS: Dual H-S-frameframeH-S-frameH-S-preframe operatorH-S-orthonormal basisMATHEMATICS SUBJECT CLASSIFICATION: 47A5842C1546C50 Additional informationFundingSupported by the Key Scientific Research Projects of Colleges and Universities in Henan Province (Grant No. 21A110004).
摘要- s -框架在本质上是一种比广义框架更一般的算子值框架。本文旨在研究H (Hilbert空间)中H- s -帧的表征和表示。首先引入H-S-preframe算子的概念，利用H-S-preframe算子对H-S-frame、Parseval H-S-frame、H-S-Riesz基、h - s -正交基和对偶H-S-frame进行了刻画，并利用H-S-preframe算子的支持得到了给定H-S-frame的所有对偶H-S-frame的精确表达式。然后通过h - s -预帧算子的性质讨论了h - s -帧的和。最后，利用框架理论的方法和技巧，给出了h - s框架和h - s -贝塞尔序列的表示。具体来说，h - s框架被表示为两个h - s标准正交基的组合的充分必要条件是h - s框架是一个H-S-Riesz基。关键词:双h - s -frameframe - s -frameframe - s -preframe算子h - s -正交基数学学科分类:47A5842C1546C50附加信息河南省高校重点科研项目(批准号21A110004)资助
{"title":"Characterizations and Representations of H-S-Frames in Hilbert Spaces","authors":"Yan-Ling Fu, Wei Zhang, Yu Tian","doi":"10.1080/01630563.2023.2259697","DOIUrl":"https://doi.org/10.1080/01630563.2023.2259697","url":null,"abstract":"AbstractH-S-frame is in essence a more general operator-valued frame than generalized frames. In this paper, we aim at studying the characterizations and representations of H-S-frames in H (Hilbert space). We first introduce the notion of H-S-preframe operator, and characterize the H-S-frames, Parseval H-S-frames, H-S-Riesz bases, H-S-orthonormal bases and dual H-S-frames with the help of H-S-preframe operators, and obtain the accurate expressions of all dual H-S-frames of a given H-S-frame by drawing support from H-S-preframe operators. Then we discuss the sum of H-S-frames through the properties of H-S-preframe operators. Finally, with the help of the approaches and skills of frame theory, we present the representations of H-S-frames and H-S-Bessel sequences. Specifically, the necessary and sufficient condition for the H-S-frame to be represented as a combination of two H-S-orthonormal bases is that the H-S-frame is an H-S-Riesz basis.KEYWORDS: Dual H-S-frameframeH-S-frameH-S-preframe operatorH-S-orthonormal basisMATHEMATICS SUBJECT CLASSIFICATION: 47A5842C1546C50 Additional informationFundingSupported by the Key Scientific Research Projects of Colleges and Universities in Henan Province (Grant No. 21A110004).","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135538597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-26DOI: 10.1080/01630563.2023.2259198
Mohamed Jleli, Bessem Samet
AbstractIn this note, we study the so-called Hermite-Hadamard inequality for the class of subharmonic functions. We first prove an inequality of this type for subharmonic functions over circular ring domains. Next, a new Hermite-Hadamard-type inequality over a disk is deduced. Moreover, we introduce the class of subharmonic functions on the coordinates, which includes the class of convex functions on the coordinates, and establish several new integral inequalities for this class of functions over various product domains: product of disks, product of circular rings and product of a disk and a circular ring.Keywords: Circular ringconvex functionsHermite Hadamard inequalitysubharmonic functionssubharmonic functions on the coordinatesMATHEMATICS SUBJECT CLASSIFICATION: 26B2526D1565D32 Disclosure statementThis work does not have any conflicts of interest.Additional informationFundingThe first author is supported by Researchers Supporting Project number (RSP2023R57), King Saud University, Riyadh, Saudi Arabia.
{"title":"On Hermite-Hadamard-Type Inequalities for Subharmonic Functions Over Circular Ring Domains","authors":"Mohamed Jleli, Bessem Samet","doi":"10.1080/01630563.2023.2259198","DOIUrl":"https://doi.org/10.1080/01630563.2023.2259198","url":null,"abstract":"AbstractIn this note, we study the so-called Hermite-Hadamard inequality for the class of subharmonic functions. We first prove an inequality of this type for subharmonic functions over circular ring domains. Next, a new Hermite-Hadamard-type inequality over a disk is deduced. Moreover, we introduce the class of subharmonic functions on the coordinates, which includes the class of convex functions on the coordinates, and establish several new integral inequalities for this class of functions over various product domains: product of disks, product of circular rings and product of a disk and a circular ring.Keywords: Circular ringconvex functionsHermite Hadamard inequalitysubharmonic functionssubharmonic functions on the coordinatesMATHEMATICS SUBJECT CLASSIFICATION: 26B2526D1565D32 Disclosure statementThis work does not have any conflicts of interest.Additional informationFundingThe first author is supported by Researchers Supporting Project number (RSP2023R57), King Saud University, Riyadh, Saudi Arabia.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134958134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-20DOI: 10.1080/01630563.2023.2254090
Chen Ling, Liqun Qi, Hong Yan
AbstractDual quaternions can represent rigid body motion in 3D spaces, and have found wide applications in robotics, 3D motion modelling and control, and computer graphics. In this paper, we introduce three different right linear independency concepts for a set of dual quaternion vectors, and study some related basic properties for dual quaternion vectors and dual quaternion matrices. We present a minimax principle for eigenvalues of dual quaternion Hermitian matrices. Based upon a newly established Cauchy-Schwarz inequality for dual quaternion vectors and singular value decomposition of dual quaternion matrices, we propose an inequality for singular values of dual quaternion matrices. Finally, we introduce the concept of generalized inverses of dual quaternion matrices, and present necessary and sufficient conditions for a dual quaternion matrix to be one of four types of generalized inverses of another dual quaternion matrix.Keywords: Dual quaternion matrixdual quaternion vectoreigenvaluegeneralized inverselinear independenceminimax principle Additional informationFundingThis work was partially supported by Hong Kong Innovation and Technology Commission (InnoHK Project CIMDA). Chen Ling’s work was supported by Natural Science Foundation of China (No. 11971138). Hong Yan’s work was supported by Hong Kong Research Grants Council (Project 11204821), Hong Kong Innovation and Technology Commission (InnoHK Project CIMDA) and City University of Hong Kong (Project 9610034).
{"title":"Minimax Principle for Eigenvalues of Dual Quaternion Hermitian Matrices and Generalized Inverses of Dual Quaternion Matrices","authors":"Chen Ling, Liqun Qi, Hong Yan","doi":"10.1080/01630563.2023.2254090","DOIUrl":"https://doi.org/10.1080/01630563.2023.2254090","url":null,"abstract":"AbstractDual quaternions can represent rigid body motion in 3D spaces, and have found wide applications in robotics, 3D motion modelling and control, and computer graphics. In this paper, we introduce three different right linear independency concepts for a set of dual quaternion vectors, and study some related basic properties for dual quaternion vectors and dual quaternion matrices. We present a minimax principle for eigenvalues of dual quaternion Hermitian matrices. Based upon a newly established Cauchy-Schwarz inequality for dual quaternion vectors and singular value decomposition of dual quaternion matrices, we propose an inequality for singular values of dual quaternion matrices. Finally, we introduce the concept of generalized inverses of dual quaternion matrices, and present necessary and sufficient conditions for a dual quaternion matrix to be one of four types of generalized inverses of another dual quaternion matrix.Keywords: Dual quaternion matrixdual quaternion vectoreigenvaluegeneralized inverselinear independenceminimax principle Additional informationFundingThis work was partially supported by Hong Kong Innovation and Technology Commission (InnoHK Project CIMDA). Chen Ling’s work was supported by Natural Science Foundation of China (No. 11971138). Hong Yan’s work was supported by Hong Kong Research Grants Council (Project 11204821), Hong Kong Innovation and Technology Commission (InnoHK Project CIMDA) and City University of Hong Kong (Project 9610034).","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136263823","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-01DOI: 10.1080/01630563.2023.2247615
Yan Tang, Zhihui Ji
Abstract In this paper, two viscosity proximal type algorithms involving the superiorization method are presented for solving the split variational inclusion problems in real Hilbert spaces. Strong convergence theorems and bounded perturbation resilience analysis of the proposed algorithms are obtained under mild conditions. The split feasibility problems, the split minimization problems, and the variational inequality problems are concerned as the applications, and several numerical experiments are performed to show the efficiency and implementation of the proposed algorithms.
{"title":"Perturbation Resilience of Self-Adaptive Step-Size Algorithms for Solving Split Variational Inclusion Problems and their Applications","authors":"Yan Tang, Zhihui Ji","doi":"10.1080/01630563.2023.2247615","DOIUrl":"https://doi.org/10.1080/01630563.2023.2247615","url":null,"abstract":"Abstract In this paper, two viscosity proximal type algorithms involving the superiorization method are presented for solving the split variational inclusion problems in real Hilbert spaces. Strong convergence theorems and bounded perturbation resilience analysis of the proposed algorithms are obtained under mild conditions. The split feasibility problems, the split minimization problems, and the variational inequality problems are concerned as the applications, and several numerical experiments are performed to show the efficiency and implementation of the proposed algorithms.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48119902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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