Pub Date : 2023-08-02DOI: 10.1080/01630563.2023.2228392
S. Lukomskii
Abstract We present a method for constructing tight wavelet frames on locally compact zero-dimensional groups. When constructing frames, we do not use the principle of unitary extension. We also consider the approximate properties of the resulting frames for functions from the Sobolev space with logarithmic weight.
{"title":"Tight wavelet frames on zero-dimensional groups. Construction and approximation","authors":"S. Lukomskii","doi":"10.1080/01630563.2023.2228392","DOIUrl":"https://doi.org/10.1080/01630563.2023.2228392","url":null,"abstract":"Abstract We present a method for constructing tight wavelet frames on locally compact zero-dimensional groups. When constructing frames, we do not use the principle of unitary extension. We also consider the approximate properties of the resulting frames for functions from the Sobolev space with logarithmic weight.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"1209 - 1227"},"PeriodicalIF":1.2,"publicationDate":"2023-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41512920","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-01DOI: 10.1080/01630563.2023.2239339
M. Eslamian, A. Kamandi
Abstract In this paper, we consider a variational inequality problem which is defined over the intersection of the set of common fixed points of a finite family of generalized demimetric mappings and the set of common zero points of a finite family of maximal monotone mappings. We propose an iterative algorithm which combines the hybrid steepest descent method with the inertial technique to solve this variational inequality problem. Strong convergence theorem of the proposed method is established under standard and mild conditions. Moreover, we do not require any prior information regarding the Lipschitz and strongly monotone constants of the mapping. The results of this paper improve and extend several known results in the literature.
{"title":"Variational Inequalities Over the Intersection of Fixed Point Sets of Generalized Demimetric Mappings and Zero Point Sets of Maximal Monotone Mappings","authors":"M. Eslamian, A. Kamandi","doi":"10.1080/01630563.2023.2239339","DOIUrl":"https://doi.org/10.1080/01630563.2023.2239339","url":null,"abstract":"Abstract In this paper, we consider a variational inequality problem which is defined over the intersection of the set of common fixed points of a finite family of generalized demimetric mappings and the set of common zero points of a finite family of maximal monotone mappings. We propose an iterative algorithm which combines the hybrid steepest descent method with the inertial technique to solve this variational inequality problem. Strong convergence theorem of the proposed method is established under standard and mild conditions. Moreover, we do not require any prior information regarding the Lipschitz and strongly monotone constants of the mapping. The results of this paper improve and extend several known results in the literature.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"1251 - 1275"},"PeriodicalIF":1.2,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47046286","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 : 2023-07-30DOI: 10.1080/01630563.2023.2234018
M. Ghadampour, E. Soori, R. Agarwal, D. O’Regan
Abstract In this paper we introduce a new projection-type algorithm in a reflexive Banach space. Then, using generalized resolvents operators and generalized projections, we prove a strong convergence theorem for computing a common element of the set of fixed points of a Bregman relatively nonexpansive mapping, solutions of an equilibrium problem, fixed points of a resolvent operator and fixed points of an infinite family of Bregman W-mappings.
{"title":"Strong Convergence Theorem Obtained by a Generalized Projections Method for Solving an Equilibrium Problem and Fixed Point Problems","authors":"M. Ghadampour, E. Soori, R. Agarwal, D. O’Regan","doi":"10.1080/01630563.2023.2234018","DOIUrl":"https://doi.org/10.1080/01630563.2023.2234018","url":null,"abstract":"Abstract In this paper we introduce a new projection-type algorithm in a reflexive Banach space. Then, using generalized resolvents operators and generalized projections, we prove a strong convergence theorem for computing a common element of the set of fixed points of a Bregman relatively nonexpansive mapping, solutions of an equilibrium problem, fixed points of a resolvent operator and fixed points of an infinite family of Bregman W-mappings.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"1153 - 1174"},"PeriodicalIF":1.2,"publicationDate":"2023-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42035779","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 : 2023-07-27DOI: 10.1080/01630563.2023.2239326
Fırat Özsaraç, A. Acu, A. Aral, I. Raşa
Abstract In this paper, we define a new generalization of Mellin-Gauss-Weierstrass operators that preserve logarithmic functions. We compute logarithmic moments of the new operators and describe the behavior of the modified operators in some weighted spaces. The weighted approximation properties of operators including weighted approximation and weighted quantitative type approximation properties, using weighted logarithmic modulus of continuity, are presented. Using the Mellin-Gauss-Weierstrass kernel as a logarithmic probability density, we study the associated information potential, the expected value and the variance .
{"title":"On the Modification of Mellin Convolution Operator and Its Associated Information Potential","authors":"Fırat Özsaraç, A. Acu, A. Aral, I. Raşa","doi":"10.1080/01630563.2023.2239326","DOIUrl":"https://doi.org/10.1080/01630563.2023.2239326","url":null,"abstract":"Abstract In this paper, we define a new generalization of Mellin-Gauss-Weierstrass operators that preserve logarithmic functions. We compute logarithmic moments of the new operators and describe the behavior of the modified operators in some weighted spaces. The weighted approximation properties of operators including weighted approximation and weighted quantitative type approximation properties, using weighted logarithmic modulus of continuity, are presented. Using the Mellin-Gauss-Weierstrass kernel as a logarithmic probability density, we study the associated information potential, the expected value and the variance .","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"1194 - 1208"},"PeriodicalIF":1.2,"publicationDate":"2023-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46319194","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 : 2023-07-26DOI: 10.1080/01630563.2023.2236690
Sh. Baharlouei, R. Mokhtari
Abstract In this paper, we extend the application of the hybridized discontinuous Galerkin (HDG) method to solve time-fractional telegraph equations. In fact, we use an HDG method for space discretization and L1 and L2 finite difference schemes using non-uniform meshes for time discretization. Thanks to a special kind of discrete Gronwall inequality, we prove that the HDG method is unconditionally stable and it is convergent with the optimal spatial order of convergence. Two numerical experiments are tested to confirm the theoretical results.
{"title":"A Stable and Convergent Hybridized Discontinuous Galerkin Method for Time-Fractional Telegraph Equations","authors":"Sh. Baharlouei, R. Mokhtari","doi":"10.1080/01630563.2023.2236690","DOIUrl":"https://doi.org/10.1080/01630563.2023.2236690","url":null,"abstract":"Abstract In this paper, we extend the application of the hybridized discontinuous Galerkin (HDG) method to solve time-fractional telegraph equations. In fact, we use an HDG method for space discretization and L1 and L2 finite difference schemes using non-uniform meshes for time discretization. Thanks to a special kind of discrete Gronwall inequality, we prove that the HDG method is unconditionally stable and it is convergent with the optimal spatial order of convergence. Two numerical experiments are tested to confirm the theoretical results.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"1175 - 1193"},"PeriodicalIF":1.2,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43475926","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 : 2023-07-15DOI: 10.1080/01630563.2023.2233585
Lê Anh Tuấn
Abstract This paper gives verifiable conditions for the existence of solutions of some set quasi-optimization problems involving Minkowski difference, where the objective maps are defined in complete metric spaces. Our proof method is not based on any scalarizing approach, and our existence results are written in terms of the given data of the problems. Several examples are provided. As applications of the main results of this paper, new results on the existence of robust solutions for uncertain multi-objective quasi-optimization problems with set-valued maps are formulated.
{"title":"Existence of Solutions of Set Quasi-Optimization Problems Involving Minkowski Difference","authors":"Lê Anh Tuấn","doi":"10.1080/01630563.2023.2233585","DOIUrl":"https://doi.org/10.1080/01630563.2023.2233585","url":null,"abstract":"Abstract This paper gives verifiable conditions for the existence of solutions of some set quasi-optimization problems involving Minkowski difference, where the objective maps are defined in complete metric spaces. Our proof method is not based on any scalarizing approach, and our existence results are written in terms of the given data of the problems. Several examples are provided. As applications of the main results of this paper, new results on the existence of robust solutions for uncertain multi-objective quasi-optimization problems with set-valued maps are formulated.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"1129 - 1152"},"PeriodicalIF":1.2,"publicationDate":"2023-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44143317","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 : 2023-07-14DOI: 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":"44 1","pages":"1097 - 1118"},"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":"44 1","pages":"1119 - 1128"},"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":"44 1","pages":"1031 - 1043"},"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":"44 1","pages":"1060 - 1093"},"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}
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