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An Approach for Solving Split Common Fixed Point Problems with Multiple Output Sets That Uses Dynamic Step Sizes 一种使用动态步长求解多输出集分裂公共不动点问题的方法
4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2023-11-10 DOI: 10.1080/01630563.2023.2278836
Huanhuan Cui
{"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}
引用次数: 0
How Averaged is the Composition of Two Linear Projections? 两个线性投影的合成有多平均?
4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2023-10-29 DOI: 10.1080/01630563.2023.2270308
Heinz H. Bauschke, Theo Bendit, Walaa M. Moursi
{"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}
引用次数: 0
An Inertial-Like Algorithm for Solving Common Fixed Point Problems of a Family of Continuous Pseudocontractive Mappings 一类连续伪压缩映射的公共不动点问题的类惯性算法
4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2023-10-27 DOI: 10.1080/01630563.2023.2267352
H. H. Gidey, H. Zegeye, O. A. Boikanyo, D. Kagiso, Y. A. Belay
{"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}
引用次数: 0
Finding the Best Proximity Point of Generalized Multivalued Contractions with Applications 广义多值压缩的最佳接近点的寻找及其应用
4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2023-10-18 DOI: 10.1080/01630563.2023.2267294
Deepesh Kumar Patel, Bhupeshwar Patel
{"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}
引用次数: 0
Strong Convergence of Trajectories via Inertial Dynamics Combining Hessian-Driven Damping and Tikhonov Regularization for General Convex Minimizations 结合hessian驱动阻尼和Tikhonov正则化的惯性动力学下轨迹的强收敛
4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2023-10-17 DOI: 10.1080/01630563.2023.2262828
Akram Chahid Bagy, Zaki Chbani, Hassan Riahi
{"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}
引用次数: 0
On Proximal Algorithms with Inertial Effects Beyond Monotonicity 超越单调性的惯性效应的近端算法
4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2023-10-13 DOI: 10.1080/01630563.2023.2266762
Alfredo N. Iusem, R. T. Marcavillaca
{"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}
引用次数: 0
Mean Inequalities for the Numerical Radius 数值半径的平均不等式
4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2023-10-13 DOI: 10.1080/01630563.2023.2265649
Fuad Kittaneh, Hamid Reza Moradi, Mohammad Sababheh
{"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}
引用次数: 0
Multivariate Zipper Fractal Functions 多元拉链分形函数
4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2023-10-12 DOI: 10.1080/01630563.2023.2265722
D. Kumar, A. K. B. Chand, P. R. Massopust
{"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}
引用次数: 0
An approach to preserve functions with exponential growth by using modified Lupaş-Kantrovich operators 利用修正lupa<e:1> - kantrovich算子保持指数增长函数的方法
4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2023-10-10 DOI: 10.1080/01630563.2023.2263977
Neha Kajla, Naokant Deo
{"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}
引用次数: 0
An Analysis on the Existence of Mild Solution and Optimal Control for Semilinear Thermoelastic System 半线性热弹性系统温和解的存在性及最优控制分析
4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2023-10-09 DOI: 10.1080/01630563.2023.2266004
Rohit Patel, V. Vijayakumar, Shimpi Singh Jadon, Anurag Shukla
{"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}
引用次数: 0
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