Pub Date : 2023-11-10DOI: 10.1080/01630563.2023.2278836
Huanhuan Cui
AbstractIn this paper, we investigate the split common fixed point problem with multiple output sets and develop novel approaches for effectively approximating its solution. We establish two convergence theorems under appropriate conditions for strictly pseudo-contractive mappings and demicontractive mappings, respectively, which cover some existing results as a special case. Furthermore, the numerical experiments demonstrate that we have developed a competitive method for solving the split common fixed point problem with multiple output sets.KEYWORDS: Demiclosedness principledemicontractive mapsplit common fixed point problemstrictly pseudo-contractive mapMATHEMATICS SUBJECT CLASSIFICATION: 47J2547H0947H1047J05 AcknowledgmentsWe would like to extend our appreciation to the reviewers for their constructive comments that significantly enhanced the quality of our work.Additional informationFundingThis work is supported by the National Natural Science Foundation of China (No. 12101286, 11971216).
{"title":"An Approach for Solving Split Common Fixed Point Problems with Multiple Output Sets That Uses Dynamic Step Sizes","authors":"Huanhuan Cui","doi":"10.1080/01630563.2023.2278836","DOIUrl":"https://doi.org/10.1080/01630563.2023.2278836","url":null,"abstract":"AbstractIn this paper, we investigate the split common fixed point problem with multiple output sets and develop novel approaches for effectively approximating its solution. We establish two convergence theorems under appropriate conditions for strictly pseudo-contractive mappings and demicontractive mappings, respectively, which cover some existing results as a special case. Furthermore, the numerical experiments demonstrate that we have developed a competitive method for solving the split common fixed point problem with multiple output sets.KEYWORDS: Demiclosedness principledemicontractive mapsplit common fixed point problemstrictly pseudo-contractive mapMATHEMATICS SUBJECT CLASSIFICATION: 47J2547H0947H1047J05 AcknowledgmentsWe would like to extend our appreciation to the reviewers for their constructive comments that significantly enhanced the quality of our work.Additional informationFundingThis work is supported by the National Natural Science Foundation of China (No. 12101286, 11971216).","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":" 988","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135185944","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 : 2023-10-29DOI: 10.1080/01630563.2023.2270308
Heinz H. Bauschke, Theo Bendit, Walaa M. Moursi
AbstractProjection operators are fundamental algorithmic operators in Analysis and Optimization. It is well known that these operators are firmly nonexpansive; however, their composition is generally only averaged and no longer firmly nonexpansive. In this note, we introduce the modulus of averagedness and provide an exact result for the composition of two linear projection operators. As a consequence, we deduce that the Ogura–Yamada bound for the modulus of the composition is sharp.KEYWORDS: Averaged mappingFriedrichs anglemodulus of averagednessnonexpansive mappingOgura–Yamada boundprojectionMATHEMATICS SUBJECT CLASSIFICATION: Primary: 47H09Secondary: 65K0590C25 AcknowledgmentsThe authors thank the reviewers and the editors for careful reading and constructive comments. We also thank Dr. Andrzej Cegielski for making us aware of his recent work [Citation3] which contains complementary results.Notes1 Usually, one excludes the cases κ = 0 and κ = 1 in the study of averaged operators, but it is very convenient in this paper to allow for this case.2 We assume for convenience throughout the paper that the operators have full domain which is the case in all algorithmic applications we are aware of. One could obviously generalize this notion to allow for operators whose domains are proper subsets of X.Additional informationFundingThe research of the authors was partially supported by Discovery Grants of the Natural Sciences and Engineering Research Council of Canada.
{"title":"How Averaged is the Composition of Two Linear Projections?","authors":"Heinz H. Bauschke, Theo Bendit, Walaa M. Moursi","doi":"10.1080/01630563.2023.2270308","DOIUrl":"https://doi.org/10.1080/01630563.2023.2270308","url":null,"abstract":"AbstractProjection operators are fundamental algorithmic operators in Analysis and Optimization. It is well known that these operators are firmly nonexpansive; however, their composition is generally only averaged and no longer firmly nonexpansive. In this note, we introduce the modulus of averagedness and provide an exact result for the composition of two linear projection operators. As a consequence, we deduce that the Ogura–Yamada bound for the modulus of the composition is sharp.KEYWORDS: Averaged mappingFriedrichs anglemodulus of averagednessnonexpansive mappingOgura–Yamada boundprojectionMATHEMATICS SUBJECT CLASSIFICATION: Primary: 47H09Secondary: 65K0590C25 AcknowledgmentsThe authors thank the reviewers and the editors for careful reading and constructive comments. We also thank Dr. Andrzej Cegielski for making us aware of his recent work [Citation3] which contains complementary results.Notes1 Usually, one excludes the cases κ = 0 and κ = 1 in the study of averaged operators, but it is very convenient in this paper to allow for this case.2 We assume for convenience throughout the paper that the operators have full domain which is the case in all algorithmic applications we are aware of. One could obviously generalize this notion to allow for operators whose domains are proper subsets of X.Additional informationFundingThe research of the authors was partially supported by Discovery Grants of the Natural Sciences and Engineering Research Council of Canada.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"67 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136134847","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 : 2023-10-27DOI: 10.1080/01630563.2023.2267352
H. H. Gidey, H. Zegeye, O. A. Boikanyo, D. Kagiso, Y. A. Belay
AbstractIn this paper, it is our purpose to introduce an inertial-like algorithm for approximating common fixed points of continuous pseudocontractive mappings in the framework of real Hilbert spaces. We prove strong convergence theorems for the sequence generated by the algorithm under certain conditions on the control sequences. We also provide numerical examples to demonstrate the efficiency of our algorithm.Keywords: Common fixed pointcontinuous mappingHilbert spaceinertial methodpseudocontaractive mappingMATHEMATICS SUBJECT CLASSIFICATION: 46N1047B0247H0547H0947H1047J2547J26 Additional informationFundingYA Belay is grateful for the financial support from Simons Foundation based at Botswana International University of Science and Technology (BIUST).
{"title":"An Inertial-Like Algorithm for Solving Common Fixed Point Problems of a Family of Continuous Pseudocontractive Mappings","authors":"H. H. Gidey, H. Zegeye, O. A. Boikanyo, D. Kagiso, Y. A. Belay","doi":"10.1080/01630563.2023.2267352","DOIUrl":"https://doi.org/10.1080/01630563.2023.2267352","url":null,"abstract":"AbstractIn this paper, it is our purpose to introduce an inertial-like algorithm for approximating common fixed points of continuous pseudocontractive mappings in the framework of real Hilbert spaces. We prove strong convergence theorems for the sequence generated by the algorithm under certain conditions on the control sequences. We also provide numerical examples to demonstrate the efficiency of our algorithm.Keywords: Common fixed pointcontinuous mappingHilbert spaceinertial methodpseudocontaractive mappingMATHEMATICS SUBJECT CLASSIFICATION: 46N1047B0247H0547H0947H1047J2547J26 Additional informationFundingYA Belay is grateful for the financial support from Simons Foundation based at Botswana International University of Science and Technology (BIUST).","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"65 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136261847","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 : 2023-10-18DOI: 10.1080/01630563.2023.2267294
Deepesh Kumar Patel, Bhupeshwar Patel
AbstractThis paper introduces new kind of algorithms for multivalued non-self mapping to obtain the best proximity point without assuming the continuity of involved mapping. Some non-trivial examples are presented to illustrate the facts. Consequently, an application to finding an optimal approximate solution for the homotopy theory is also discussed.Keywords: Best proximity pointFeng-Liu type F-contractionmultivalued almost F-contractionweak P-property and homotopyMATHEMATICS SUBJECT CLASSIFICATION: 47H1054H2554E50 AcknowledgmentsThe authors would like to thank the editor and reviewers for their valuable comments.
{"title":"Finding the Best Proximity Point of Generalized Multivalued Contractions with Applications","authors":"Deepesh Kumar Patel, Bhupeshwar Patel","doi":"10.1080/01630563.2023.2267294","DOIUrl":"https://doi.org/10.1080/01630563.2023.2267294","url":null,"abstract":"AbstractThis paper introduces new kind of algorithms for multivalued non-self mapping to obtain the best proximity point without assuming the continuity of involved mapping. Some non-trivial examples are presented to illustrate the facts. Consequently, an application to finding an optimal approximate solution for the homotopy theory is also discussed.Keywords: Best proximity pointFeng-Liu type F-contractionmultivalued almost F-contractionweak P-property and homotopyMATHEMATICS SUBJECT CLASSIFICATION: 47H1054H2554E50 AcknowledgmentsThe authors would like to thank the editor and reviewers for their valuable comments.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135884779","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 : 2023-10-17DOI: 10.1080/01630563.2023.2262828
Akram Chahid Bagy, Zaki Chbani, Hassan Riahi
AbstractLet H be a real Hilbert space, and f:H→R be a convex twice differentiable function whose solution set argminf is nonempty. We investigate the long time behavior of the trajectories of the vanishing damped dynamical system with Tikhonov regularizing term and Hessian-driven damping x¨(t)+α x˙(t)+δ∇2f(x(t))x˙(t)+β(t)∇f(x(t))+cx(t)=0 where α,c,δ are three positive constants, and the time scale parameter β is a positive nondecreasing function such that limt→+∞β(t)=+∞. Under some assumptions on the parameter β, we will show rapid convergence of values, strong convergence toward the minimum norm element of argminf, and rapid convergence of the gradients toward zero. Note that the Hessian-driven damping significantly reduces the oscillatory aspects, and the time scale parameter β improves the rate of convergences mentioned above. As particular cases of β, we set β(t)=tp ln q(t), for (p,q)∈(R+)2∖{(0,0)}, and β(t)=eγtp, for p∈]0,1[ and γ>0. The manuscript concludes with two numerical examples and comments on their performance.KEYWORDS: Damped dynamical systemfast convergenceHessian-driven dampingHilbert spacestrong convergenceTikhonov regularizationMATHEMATICS SUBJECT CLASSIFICATION: 37N4046N1049M3065K0565K1090B5090C25
{"title":"Strong Convergence of Trajectories via Inertial Dynamics Combining Hessian-Driven Damping and Tikhonov Regularization for General Convex Minimizations","authors":"Akram Chahid Bagy, Zaki Chbani, Hassan Riahi","doi":"10.1080/01630563.2023.2262828","DOIUrl":"https://doi.org/10.1080/01630563.2023.2262828","url":null,"abstract":"AbstractLet H be a real Hilbert space, and f:H→R be a convex twice differentiable function whose solution set argminf is nonempty. We investigate the long time behavior of the trajectories of the vanishing damped dynamical system with Tikhonov regularizing term and Hessian-driven damping x¨(t)+α x˙(t)+δ∇2f(x(t))x˙(t)+β(t)∇f(x(t))+cx(t)=0 where α,c,δ are three positive constants, and the time scale parameter β is a positive nondecreasing function such that limt→+∞β(t)=+∞. Under some assumptions on the parameter β, we will show rapid convergence of values, strong convergence toward the minimum norm element of argminf, and rapid convergence of the gradients toward zero. Note that the Hessian-driven damping significantly reduces the oscillatory aspects, and the time scale parameter β improves the rate of convergences mentioned above. As particular cases of β, we set β(t)=tp ln q(t), for (p,q)∈(R+)2∖{(0,0)}, and β(t)=eγtp, for p∈]0,1[ and γ>0. The manuscript concludes with two numerical examples and comments on their performance.KEYWORDS: Damped dynamical systemfast convergenceHessian-driven dampingHilbert spacestrong convergenceTikhonov regularizationMATHEMATICS SUBJECT CLASSIFICATION: 37N4046N1049M3065K0565K1090B5090C25","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"31 6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136032651","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 : 2023-10-13DOI: 10.1080/01630563.2023.2266762
Alfredo N. Iusem, R. T. Marcavillaca
AbstractInertial procedures attached to classical methods for solving monotone inclusion and optimization problems, which arise from an implicit discretization of second-order differential equations, have shown a remarkable acceleration effect with respect to these classical algorithms. Among these classical methods, one can mention steepest descent, alternate directions, and the proximal point methods. For the problem of finding zeroes of set-valued operators, the convergence analysis of all existing inertial-proximal methods requires the monotonicity of the operator. We present here a new inertial-proximal point algorithm for finding zeroes of set-valued operators, whose convergence is established for a relevant class of nonmonotone operators, namely the hypomonotone ones.KEYWORDS: Generalized monotone operatorshypomonotone operatorsinertial methodsproximal point methodMATHEMATICS SUBJECT CLASSIFICATION: 90C2590C3047H05
{"title":"On Proximal Algorithms with Inertial Effects Beyond Monotonicity","authors":"Alfredo N. Iusem, R. T. Marcavillaca","doi":"10.1080/01630563.2023.2266762","DOIUrl":"https://doi.org/10.1080/01630563.2023.2266762","url":null,"abstract":"AbstractInertial procedures attached to classical methods for solving monotone inclusion and optimization problems, which arise from an implicit discretization of second-order differential equations, have shown a remarkable acceleration effect with respect to these classical algorithms. Among these classical methods, one can mention steepest descent, alternate directions, and the proximal point methods. For the problem of finding zeroes of set-valued operators, the convergence analysis of all existing inertial-proximal methods requires the monotonicity of the operator. We present here a new inertial-proximal point algorithm for finding zeroes of set-valued operators, whose convergence is established for a relevant class of nonmonotone operators, namely the hypomonotone ones.KEYWORDS: Generalized monotone operatorshypomonotone operatorsinertial methodsproximal point methodMATHEMATICS SUBJECT CLASSIFICATION: 90C2590C3047H05","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135859122","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 : 2023-10-13DOI: 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":"53 1","pages":"0"},"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":"8 1","pages":"0"},"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":"41 1","pages":"0"},"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":"26 1","pages":"0"},"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}
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