Pub Date : 2023-07-14DOI: 10.1080/01630563.2023.2221897
C. Conde, Kais Feki, F. Kittaneh
Abstract Our aim in this article is to establish several new norm and numerical radius inequalities for products and sums of operators acting on a complex Hilbert space . Some of the obtained inequalities improve well known ones. In addition, by using new techniques, we prove certain new inequalities related to and , where and denote the A-numerical radius and the A-operator seminorm of an operator T acting on the semi-Hilbert space respectively. Here for every .
{"title":"Further Seminorm and Numerical Radius Inequalities for Products and Sums of Operators","authors":"C. Conde, Kais Feki, F. Kittaneh","doi":"10.1080/01630563.2023.2221897","DOIUrl":"https://doi.org/10.1080/01630563.2023.2221897","url":null,"abstract":"Abstract Our aim in this article is to establish several new norm and numerical radius inequalities for products and sums of operators acting on a complex Hilbert space . Some of the obtained inequalities improve well known ones. In addition, by using new techniques, we prove certain new inequalities related to and , where and denote the A-numerical radius and the A-operator seminorm of an operator T acting on the semi-Hilbert space respectively. Here for every .","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44182881","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 : 2023-07-13DOI: 10.1080/01630563.2023.2233168
I. Dali, M. B. Moustaid
Abstract In this paper, we deal with vector equilibrium problems. We prove the nonemptiness of the solution set for this type of problems in the sequential compactness case and in the absence of convexity and lower semicontinuity assumptions. Some examples are presented and an existence result for countable systems of vector equilibrium problems is stated.
{"title":"A New Existence Result of Equilibria for Vector Equilibrium Problems","authors":"I. Dali, M. B. Moustaid","doi":"10.1080/01630563.2023.2233168","DOIUrl":"https://doi.org/10.1080/01630563.2023.2233168","url":null,"abstract":"Abstract In this paper, we deal with vector equilibrium problems. We prove the nonemptiness of the solution set for this type of problems in the sequential compactness case and in the absence of convexity and lower semicontinuity assumptions. Some examples are presented and an existence result for countable systems of vector equilibrium problems is stated.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41528217","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 : 2023-07-03DOI: 10.1080/01630563.2023.2221896
Huimin He, Jigen Peng, Qinwei Fan
Abstract In this paper, we propose a novel Halpern-type algorithm and prove that the sequence generated by the algorithm converges strongly to the common element of the set of fixed points of the two firmly nonexpansive mappings and the solution set of zero points of the monotone inclusion problems on Hadamard manifolds, the main results in this paper extended and improved some recent related results.
{"title":"A Novel Halpern-type Algorithm for a Monotone Inclusion Problem and a Fixed Points Problem on Hadamard Manifolds","authors":"Huimin He, Jigen Peng, Qinwei Fan","doi":"10.1080/01630563.2023.2221896","DOIUrl":"https://doi.org/10.1080/01630563.2023.2221896","url":null,"abstract":"Abstract In this paper, we propose a novel Halpern-type algorithm and prove that the sequence generated by the algorithm converges strongly to the common element of the set of fixed points of the two firmly nonexpansive mappings and the solution set of zero points of the monotone inclusion problems on Hadamard manifolds, the main results in this paper extended and improved some recent related results.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41772604","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 : 2023-07-03DOI: 10.1080/01630563.2023.2227973
F. Margotti
Abstract This article generalizes the results of the so-called linear functional strategy [R. S. Anderssen, Inverse Problems (Oberwolfach, 1986)], used for fast reconstruction of some particular feature of interest in the solution of a linear inverse problem. Two versions are proposed for nonlinear problems. The first one applies to differentiable forward operators and is based on the One-Step Newton method. The second one, in turn, uses a linearization of the forward operator obtained by the employment of basic Machine Learning techniques, being applicable to non-differentiable operators. As a byproduct of the proposed methods, we derive two variants of the so-called approximate inverse method [A. K. Louis, Inverse Problems, 1996] for nonlinear inverse problems. Numerical tests, using electrical impedance tomography applied to a biphasic flow problem, are presented to test the efficiency of the proposed methods.
{"title":"Linear Functional Strategy and the Approximate Inverse for Nonlinear Ill-Posed Problems","authors":"F. Margotti","doi":"10.1080/01630563.2023.2227973","DOIUrl":"https://doi.org/10.1080/01630563.2023.2227973","url":null,"abstract":"Abstract This article generalizes the results of the so-called linear functional strategy [R. S. Anderssen, Inverse Problems (Oberwolfach, 1986)], used for fast reconstruction of some particular feature of interest in the solution of a linear inverse problem. Two versions are proposed for nonlinear problems. The first one applies to differentiable forward operators and is based on the One-Step Newton method. The second one, in turn, uses a linearization of the forward operator obtained by the employment of basic Machine Learning techniques, being applicable to non-differentiable operators. As a byproduct of the proposed methods, we derive two variants of the so-called approximate inverse method [A. K. Louis, Inverse Problems, 1996] for nonlinear inverse problems. Numerical tests, using electrical impedance tomography applied to a biphasic flow problem, are presented to test the efficiency of the proposed methods.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49204589","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 : 2023-06-28DOI: 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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}
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