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":"11 1","pages":"0"},"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":"1 1","pages":"0"},"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":"42 1","pages":"0"},"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":"61 1","pages":"0"},"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":"161 1","pages":"0"},"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":"44 1","pages":"1343 - 1370"},"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}
Pub Date : 2023-08-23DOI: 10.1080/01630563.2023.2248695
Vakeel A. Khan, Mohammad Daud Khan, Amit Kumar
ABSTRACTIn this article, we study the statistical convergence of sequences of functions in neutrosophic normed spaces. We define the concept of statistical pointwise convergence and statistical uniform convergence in neutrosophic normed spaces and give some basic properties of these concepts.KEYWORDS: Neutrosophic normed space-(NNS)statistically Cauchy sequencesstatistically completeness and uniformly statistically convergentstatistical convergent AcknowledgmentsWe would like to express our gratitude to the referees of the paper for their useful comments and suggestions toward the quality improvement of the paper.
{"title":"Statistical Convergence of Sequences of Functions in Neutrosophic Normed Spaces","authors":"Vakeel A. Khan, Mohammad Daud Khan, Amit Kumar","doi":"10.1080/01630563.2023.2248695","DOIUrl":"https://doi.org/10.1080/01630563.2023.2248695","url":null,"abstract":"ABSTRACTIn this article, we study the statistical convergence of sequences of functions in neutrosophic normed spaces. We define the concept of statistical pointwise convergence and statistical uniform convergence in neutrosophic normed spaces and give some basic properties of these concepts.KEYWORDS: Neutrosophic normed space-(NNS)statistically Cauchy sequencesstatistically completeness and uniformly statistically convergentstatistical convergent AcknowledgmentsWe would like to express our gratitude to the referees of the paper for their useful comments and suggestions toward the quality improvement of the paper.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135570344","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 : 2023-08-17DOI: 10.1080/01630563.2023.2241146
H. Özgen
Abstract– In this paper, we have generalized two known theorems dealing with the absolute weighted arithmetic mean summability factors of infinite series and Fourier series to the absolute matrix summability methods. Some new and known results have also been obtained.
{"title":"On Absolute Matrix Summability of Factored Infinite Series and Fourier Series","authors":"H. Özgen","doi":"10.1080/01630563.2023.2241146","DOIUrl":"https://doi.org/10.1080/01630563.2023.2241146","url":null,"abstract":"Abstract– In this paper, we have generalized two known theorems dealing with the absolute weighted arithmetic mean summability factors of infinite series and Fourier series to the absolute matrix summability methods. Some new and known results have also been obtained.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"1300 - 1308"},"PeriodicalIF":1.2,"publicationDate":"2023-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42267301","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 : 2023-08-04DOI: 10.1080/01630563.2023.2235614
V. Vivanco-Orellana, R. Osuna-Gómez, M. Rojas-Medar
Abstract We derive new necessary and sufficient optimality conditions for optimization problems with multi-equality and inequality constraints through the Dubovitskii-Milyutin formalism, characterizing the feasible and tangent directions cones in a neighborhood of a non-regular point. We also establish conditions of 2-regularity under which necessary optimality conditions are non-degenerate. These conditions apply when the phenomenon of non-regularity (or abnormality) take place. In addition examples that illustrate our results are presented.
{"title":"Necessary and Sufficient Optimality Conditions for Non-regular Problems","authors":"V. Vivanco-Orellana, R. Osuna-Gómez, M. Rojas-Medar","doi":"10.1080/01630563.2023.2235614","DOIUrl":"https://doi.org/10.1080/01630563.2023.2235614","url":null,"abstract":"Abstract We derive new necessary and sufficient optimality conditions for optimization problems with multi-equality and inequality constraints through the Dubovitskii-Milyutin formalism, characterizing the feasible and tangent directions cones in a neighborhood of a non-regular point. We also establish conditions of 2-regularity under which necessary optimality conditions are non-degenerate. These conditions apply when the phenomenon of non-regularity (or abnormality) take place. In addition examples that illustrate our results are presented.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"1228 - 1250"},"PeriodicalIF":1.2,"publicationDate":"2023-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47567635","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 : 2023-08-04DOI: 10.1080/01630563.2023.2241143
D. Costarelli, Maria Gabriella Natale, G. Vinti
Abstract In the present paper, convergence in modular spaces is investigated for a class of nonlinear discrete operators, namely the nonlinear multivariate sampling Kantorovich operators. The convergence results in the Musielak-Orlicz spaces, in the weighted Orlicz spaces, and in the Orlicz spaces follow as particular cases. Even more, spaces of functions equipped by modulars without an integral representation are presented and discussed.
{"title":"Convergence Results for Nonlinear Sampling Kantorovich Operators in Modular Spaces","authors":"D. Costarelli, Maria Gabriella Natale, G. Vinti","doi":"10.1080/01630563.2023.2241143","DOIUrl":"https://doi.org/10.1080/01630563.2023.2241143","url":null,"abstract":"Abstract In the present paper, convergence in modular spaces is investigated for a class of nonlinear discrete operators, namely the nonlinear multivariate sampling Kantorovich operators. The convergence results in the Musielak-Orlicz spaces, in the weighted Orlicz spaces, and in the Orlicz spaces follow as particular cases. Even more, spaces of functions equipped by modulars without an integral representation are presented and discussed.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"1276 - 1299"},"PeriodicalIF":1.2,"publicationDate":"2023-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42129373","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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