Pub Date : 2023-06-28DOI: 10.1080/01630563.2023.2221856
S. Reich, Truong Minh Tuyen, P. T. Huyen
Abstract We introduce new self-adaptive algorithms for solving the split common zero point problem with multiple output sets in Hilbert space. We also apply our main results to solving split feasibility problems with multiple output sets.
{"title":"New Algorithms for Solving the Split Common Zero Point Problem in Hilbert Space","authors":"S. Reich, Truong Minh Tuyen, P. T. Huyen","doi":"10.1080/01630563.2023.2221856","DOIUrl":"https://doi.org/10.1080/01630563.2023.2221856","url":null,"abstract":"Abstract We introduce new self-adaptive algorithms for solving the split common zero point problem with multiple output sets in Hilbert space. We also apply our main results to solving split feasibility problems with multiple output sets.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"1012 - 1030"},"PeriodicalIF":1.2,"publicationDate":"2023-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42584128","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 : 2023-06-23DOI: 10.1080/01630563.2023.2221898
J. Baldonedo, J. Fernández, R. Quintanilla
Abstract In this work, we study a new thermoelastic model with two temperatures from the numerical point of view. The problem is written as a coupled linear system whose unknowns are the displacement field and the conductivity and thermodynamic temperatures. An existence and uniqueness result recently proved is recalled. Then, a fully discrete approximation is introduced by using the finite element method and the classical implicit Euler scheme. A main a priori error estimates result is proved and, under some appropriate regularity conditions on the continuous solution, we obtain the linear convergence. Finally, some numerical simulations are presented to demonstrate the numerical convergence and the discrete energy decay.
{"title":"A Fully Discrete Approximation of a New Two-Temperature Thermoelastic Model","authors":"J. Baldonedo, J. Fernández, R. Quintanilla","doi":"10.1080/01630563.2023.2221898","DOIUrl":"https://doi.org/10.1080/01630563.2023.2221898","url":null,"abstract":"Abstract In this work, we study a new thermoelastic model with two temperatures from the numerical point of view. The problem is written as a coupled linear system whose unknowns are the displacement field and the conductivity and thermodynamic temperatures. An existence and uniqueness result recently proved is recalled. Then, a fully discrete approximation is introduced by using the finite element method and the classical implicit Euler scheme. A main a priori error estimates result is proved and, under some appropriate regularity conditions on the continuous solution, we obtain the linear convergence. Finally, some numerical simulations are presented to demonstrate the numerical convergence and the discrete energy decay.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"1044 - 1059"},"PeriodicalIF":1.2,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48660858","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 : 2023-06-14DOI: 10.1080/01630563.2023.2221857
Pintu Bhunia, M. Gürdal, K. Paul, A. Sen, R. Tapdigoglu
Abstract In this paper, we provide a new norm(α-Berezin norm) on the space of all bounded linear operators defined on a reproducing kernel Hilbert space, which generalizes the Berezin radius and the Berezin norm. We study the basic properties of the α-Berezin norm and develop various inequalities involving the α-Berezin norm. By using the inequalities we obtain various bounds for the Berezin radius of bounded linear operators, which improve on the earlier bounds. Further, we obtain a Berezin radius inequality for the sum of the product of operators, from which we derive new Berezin radius bounds.
{"title":"On a New Norm on the Space of Reproducing Kernel Hilbert Space Operators and Berezin Radius Inequalities","authors":"Pintu Bhunia, M. Gürdal, K. Paul, A. Sen, R. Tapdigoglu","doi":"10.1080/01630563.2023.2221857","DOIUrl":"https://doi.org/10.1080/01630563.2023.2221857","url":null,"abstract":"Abstract In this paper, we provide a new norm(α-Berezin norm) on the space of all bounded linear operators defined on a reproducing kernel Hilbert space, which generalizes the Berezin radius and the Berezin norm. We study the basic properties of the α-Berezin norm and develop various inequalities involving the α-Berezin norm. By using the inequalities we obtain various bounds for the Berezin radius of bounded linear operators, which improve on the earlier bounds. Further, we obtain a Berezin radius inequality for the sum of the product of operators, from which we derive new Berezin radius bounds.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"970 - 986"},"PeriodicalIF":1.2,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47501023","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 : 2023-06-11DOI: 10.1080/01630563.2023.2209150
Zhan-jie Song, Shuo Zhang
Abstract In this article, we consider the extension of Shannon sampling series reconstruction theorem for nonhomogeneous random fields using local averages sampling, which helps improve certain earlier results. The upper bound of mean square truncation sampling approximation error is more precise, and we establish one approximation result in the almost sure sense.
{"title":"Approximation of Nonhomogeneous Random Field from Local Averages","authors":"Zhan-jie Song, Shuo Zhang","doi":"10.1080/01630563.2023.2209150","DOIUrl":"https://doi.org/10.1080/01630563.2023.2209150","url":null,"abstract":"Abstract In this article, we consider the extension of Shannon sampling series reconstruction theorem for nonhomogeneous random fields using local averages sampling, which helps improve certain earlier results. The upper bound of mean square truncation sampling approximation error is more precise, and we establish one approximation result in the almost sure sense.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"743 - 763"},"PeriodicalIF":1.2,"publicationDate":"2023-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46550189","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 : 2023-06-05DOI: 10.1080/01630563.2023.2217893
A. Orzan, R. Precup
Abstract In this paper we establish some approximation versions of the classical Dinkelbach algorithm for nonlinear fractional optimization problems in Banach spaces. We start by examining what occurs if at any step of the algorithm, the generated point desired to be a minimizer can only be determined with a given error. Next we assume that the step error tends to zero as the algorithm advances. The last version of the algorithm we present is making use of Ekeland’s variational principle for generating the sequence of minimizer-like points. In the final part of the article we deliver some results in order to achieve a Palais-Smale type compactness condition that guarantees the convergence of our Dinkelbach-Ekeland algorithm.
{"title":"Dinkelbach Type Approximation Algorithms for Nonlinear Fractional Optimization Problems","authors":"A. Orzan, R. Precup","doi":"10.1080/01630563.2023.2217893","DOIUrl":"https://doi.org/10.1080/01630563.2023.2217893","url":null,"abstract":"Abstract In this paper we establish some approximation versions of the classical Dinkelbach algorithm for nonlinear fractional optimization problems in Banach spaces. We start by examining what occurs if at any step of the algorithm, the generated point desired to be a minimizer can only be determined with a given error. Next we assume that the step error tends to zero as the algorithm advances. The last version of the algorithm we present is making use of Ekeland’s variational principle for generating the sequence of minimizer-like points. In the final part of the article we deliver some results in order to achieve a Palais-Smale type compactness condition that guarantees the convergence of our Dinkelbach-Ekeland algorithm.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"954 - 969"},"PeriodicalIF":1.2,"publicationDate":"2023-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49418204","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 : 2023-05-22DOI: 10.1080/01630563.2023.2212494
Shouguo Zhu
Abstract This article analyzes a Caputo type fractional backward nonlocal evolution control system. By means of a joint combination of resolvent theory with the approximation solvability technique, we dispense with the compactness assumption on the semigroup and the Lipschitz restriction on the nonlinear term when we treat the existence of solutions. Furthermore, we launch a new method of formulating minimizing sequences twice and the weak topology technique to explore the optimal control problem (OP). Finally, the plausibility of our mentioned results is supported by a simple application.
{"title":"Optimal Controls for Fractional Backward Nonlocal Evolution Systems","authors":"Shouguo Zhu","doi":"10.1080/01630563.2023.2212494","DOIUrl":"https://doi.org/10.1080/01630563.2023.2212494","url":null,"abstract":"Abstract This article analyzes a Caputo type fractional backward nonlocal evolution control system. By means of a joint combination of resolvent theory with the approximation solvability technique, we dispense with the compactness assumption on the semigroup and the Lipschitz restriction on the nonlinear term when we treat the existence of solutions. Furthermore, we launch a new method of formulating minimizing sequences twice and the weak topology technique to explore the optimal control problem (OP). Finally, the plausibility of our mentioned results is supported by a simple application.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"794 - 814"},"PeriodicalIF":1.2,"publicationDate":"2023-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43285120","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 : 2023-05-21DOI: 10.1080/01630563.2023.2209161
Yan Zhang, Yun‐Zhang Li
Abstract Due to being a group under Walsh addition ⊕, the wavelet frame theory on has been well developed in recent years. This paper addresses wavelet dual frames on Sobolev spaces defined on We introduce the Sobolev space with characterize (weak) nonhomogeneous wavelet dual frames for and establish mixed oblique extension principles for constructing them.
{"title":"A Characterization of (Weak) Nonhomogeneous Wavelet Dual Frames and Mixed Oblique Principle in Sobolev Spaces on the Half Real Line","authors":"Yan Zhang, Yun‐Zhang Li","doi":"10.1080/01630563.2023.2209161","DOIUrl":"https://doi.org/10.1080/01630563.2023.2209161","url":null,"abstract":"Abstract Due to being a group under Walsh addition ⊕, the wavelet frame theory on has been well developed in recent years. This paper addresses wavelet dual frames on Sobolev spaces defined on We introduce the Sobolev space with characterize (weak) nonhomogeneous wavelet dual frames for and establish mixed oblique extension principles for constructing them.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"764 - 793"},"PeriodicalIF":1.2,"publicationDate":"2023-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49510612","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 : 2023-05-19DOI: 10.1080/01630563.2023.2212495
R. Gholipour, M. Gabeleh, H. Mazaheri
Abstract We consider a new type of cyclic (noncyclic) mappings, called diametrically relatively nonexpansive maps which contains properly the class of cyclic (noncyclic) relatively nonexpansive mappings. For such mappings we obtain existence results of best proximity points (pairs) in the framework of Busemann convex spaces and generalize the recent conclusions in this direction. We also present a characterization of proximal normal structure in term of best proximity points (pairs) for diametrically relatively nonexpansive mappings.
{"title":"Diametrically Relatively Nonexpansive Mappings and a Characterization of Proximal Normal Structure","authors":"R. Gholipour, M. Gabeleh, H. Mazaheri","doi":"10.1080/01630563.2023.2212495","DOIUrl":"https://doi.org/10.1080/01630563.2023.2212495","url":null,"abstract":"Abstract We consider a new type of cyclic (noncyclic) mappings, called diametrically relatively nonexpansive maps which contains properly the class of cyclic (noncyclic) relatively nonexpansive mappings. For such mappings we obtain existence results of best proximity points (pairs) in the framework of Busemann convex spaces and generalize the recent conclusions in this direction. We also present a characterization of proximal normal structure in term of best proximity points (pairs) for diametrically relatively nonexpansive mappings.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"815 - 840"},"PeriodicalIF":1.2,"publicationDate":"2023-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42758622","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 : 2023-05-19DOI: 10.1080/01630563.2023.2212496
El‐Hassan Benkhira, R. Fakhar, Y. Mandyly
Abstract The effects of an included temperature field in the contact process between a piezoelectric body and a rigid foundation with thermal and electrical conductivity are discussed. The constitutive relation of the material is assumed to be thermo-electro-elastic and involves the nonlinear elastic constitutive Hencky’s law. The frictional contact is modeled with Signorini’s conditions, the regularized Coulomb law, and the regularized electrical and thermal conductivity conditions. The resulting thermo-electromechanical model includes the temperature field as an additional state variable to take into account thermal effects alongside with those of the piezoelectric. The existence of the unique weak solution to the problem is established by using Schauder’s fixed point theorem combined with arguments from the theory of variational inequalities involving nonlinear strongly monotone Lipschitz continuous operators. A successive iteration technique to solve the problem numerically is proposed, and its convergence is established. A variant of the Augmented Lagrangian, the so-called Alternating Direction Method of multipliers (ADMM), is used to decompose the original problem into two sub-problems, solve them sequentially and update the dual variables at each iteration. The influence of the thermal boundary condition on the behavior of contact forces and electrical potential is shown through graphical illustrations.
{"title":"Analysis and Numerical Approach of a Coupled Thermo-Electro-Mechanical System for Nonlinear Hencky-Type Materials with Nonlocal Coulomb’s Friction","authors":"El‐Hassan Benkhira, R. Fakhar, Y. Mandyly","doi":"10.1080/01630563.2023.2212496","DOIUrl":"https://doi.org/10.1080/01630563.2023.2212496","url":null,"abstract":"Abstract The effects of an included temperature field in the contact process between a piezoelectric body and a rigid foundation with thermal and electrical conductivity are discussed. The constitutive relation of the material is assumed to be thermo-electro-elastic and involves the nonlinear elastic constitutive Hencky’s law. The frictional contact is modeled with Signorini’s conditions, the regularized Coulomb law, and the regularized electrical and thermal conductivity conditions. The resulting thermo-electromechanical model includes the temperature field as an additional state variable to take into account thermal effects alongside with those of the piezoelectric. The existence of the unique weak solution to the problem is established by using Schauder’s fixed point theorem combined with arguments from the theory of variational inequalities involving nonlinear strongly monotone Lipschitz continuous operators. A successive iteration technique to solve the problem numerically is proposed, and its convergence is established. A variant of the Augmented Lagrangian, the so-called Alternating Direction Method of multipliers (ADMM), is used to decompose the original problem into two sub-problems, solve them sequentially and update the dual variables at each iteration. The influence of the thermal boundary condition on the behavior of contact forces and electrical potential is shown through graphical illustrations.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"841 - 866"},"PeriodicalIF":1.2,"publicationDate":"2023-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42375955","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 : 2023-05-13DOI: 10.1080/01630563.2023.2208868
Maisam Boroun, S. Heidarkhani
Abstract In this article, we are concerned with the existence of at least one, two and three distinct solutions for discrete boundary value problems driven by the Laplacian. The proof of the main result depends on variational methods. By using a consequence of the local minimum theorem due Bonanno we investigate the existence of at least one solution and two solutions for the problem with the weight. Furthermore, by using two critical point theorems, one due Averna and Bonanno, and another due Bonanno we explore the existence of two and three solutions for the problem. We also provide two examples in order to illustrate the main results.
{"title":"Variational Approaches to a Discrete Elliptic Problem with a Weight","authors":"Maisam Boroun, S. Heidarkhani","doi":"10.1080/01630563.2023.2208868","DOIUrl":"https://doi.org/10.1080/01630563.2023.2208868","url":null,"abstract":"Abstract In this article, we are concerned with the existence of at least one, two and three distinct solutions for discrete boundary value problems driven by the Laplacian. The proof of the main result depends on variational methods. By using a consequence of the local minimum theorem due Bonanno we investigate the existence of at least one solution and two solutions for the problem with the weight. Furthermore, by using two critical point theorems, one due Averna and Bonanno, and another due Bonanno we explore the existence of two and three solutions for the problem. We also provide two examples in order to illustrate the main results.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"724 - 742"},"PeriodicalIF":1.2,"publicationDate":"2023-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45281071","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：