Pub Date : 2023-08-23DOI: 10.1080/01630563.2023.2248695
Vakeel A. Khan, Mohammad Daud Khan, Amit Kumar
ABSTRACTIn this article, we study the statistical convergence of sequences of functions in neutrosophic normed spaces. We define the concept of statistical pointwise convergence and statistical uniform convergence in neutrosophic normed spaces and give some basic properties of these concepts.KEYWORDS: Neutrosophic normed space-(NNS)statistically Cauchy sequencesstatistically completeness and uniformly statistically convergentstatistical convergent AcknowledgmentsWe would like to express our gratitude to the referees of the paper for their useful comments and suggestions toward the quality improvement of the paper.
{"title":"Statistical Convergence of Sequences of Functions in Neutrosophic Normed Spaces","authors":"Vakeel A. Khan, Mohammad Daud Khan, Amit Kumar","doi":"10.1080/01630563.2023.2248695","DOIUrl":"https://doi.org/10.1080/01630563.2023.2248695","url":null,"abstract":"ABSTRACTIn this article, we study the statistical convergence of sequences of functions in neutrosophic normed spaces. We define the concept of statistical pointwise convergence and statistical uniform convergence in neutrosophic normed spaces and give some basic properties of these concepts.KEYWORDS: Neutrosophic normed space-(NNS)statistically Cauchy sequencesstatistically completeness and uniformly statistically convergentstatistical convergent AcknowledgmentsWe would like to express our gratitude to the referees of the paper for their useful comments and suggestions toward the quality improvement of the paper.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135570344","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 : 2023-08-17DOI: 10.1080/01630563.2023.2241146
H. Özgen
Abstract– In this paper, we have generalized two known theorems dealing with the absolute weighted arithmetic mean summability factors of infinite series and Fourier series to the absolute matrix summability methods. Some new and known results have also been obtained.
{"title":"On Absolute Matrix Summability of Factored Infinite Series and Fourier Series","authors":"H. Özgen","doi":"10.1080/01630563.2023.2241146","DOIUrl":"https://doi.org/10.1080/01630563.2023.2241146","url":null,"abstract":"Abstract– In this paper, we have generalized two known theorems dealing with the absolute weighted arithmetic mean summability factors of infinite series and Fourier series to the absolute matrix summability methods. Some new and known results have also been obtained.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42267301","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 : 2023-08-04DOI: 10.1080/01630563.2023.2235614
V. Vivanco-Orellana, R. Osuna-Gómez, M. Rojas-Medar
Abstract We derive new necessary and sufficient optimality conditions for optimization problems with multi-equality and inequality constraints through the Dubovitskii-Milyutin formalism, characterizing the feasible and tangent directions cones in a neighborhood of a non-regular point. We also establish conditions of 2-regularity under which necessary optimality conditions are non-degenerate. These conditions apply when the phenomenon of non-regularity (or abnormality) take place. In addition examples that illustrate our results are presented.
{"title":"Necessary and Sufficient Optimality Conditions for Non-regular Problems","authors":"V. Vivanco-Orellana, R. Osuna-Gómez, M. Rojas-Medar","doi":"10.1080/01630563.2023.2235614","DOIUrl":"https://doi.org/10.1080/01630563.2023.2235614","url":null,"abstract":"Abstract We derive new necessary and sufficient optimality conditions for optimization problems with multi-equality and inequality constraints through the Dubovitskii-Milyutin formalism, characterizing the feasible and tangent directions cones in a neighborhood of a non-regular point. We also establish conditions of 2-regularity under which necessary optimality conditions are non-degenerate. These conditions apply when the phenomenon of non-regularity (or abnormality) take place. In addition examples that illustrate our results are presented.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47567635","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 : 2023-08-04DOI: 10.1080/01630563.2023.2241143
D. Costarelli, Maria Gabriella Natale, G. Vinti
Abstract In the present paper, convergence in modular spaces is investigated for a class of nonlinear discrete operators, namely the nonlinear multivariate sampling Kantorovich operators. The convergence results in the Musielak-Orlicz spaces, in the weighted Orlicz spaces, and in the Orlicz spaces follow as particular cases. Even more, spaces of functions equipped by modulars without an integral representation are presented and discussed.
{"title":"Convergence Results for Nonlinear Sampling Kantorovich Operators in Modular Spaces","authors":"D. Costarelli, Maria Gabriella Natale, G. Vinti","doi":"10.1080/01630563.2023.2241143","DOIUrl":"https://doi.org/10.1080/01630563.2023.2241143","url":null,"abstract":"Abstract In the present paper, convergence in modular spaces is investigated for a class of nonlinear discrete operators, namely the nonlinear multivariate sampling Kantorovich operators. The convergence results in the Musielak-Orlicz spaces, in the weighted Orlicz spaces, and in the Orlicz spaces follow as particular cases. Even more, spaces of functions equipped by modulars without an integral representation are presented and discussed.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42129373","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 : 2023-08-02DOI: 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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}
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