Pub Date : 2023-01-24DOI: 10.1080/01630563.2023.2167088
G. Yuan
Abstract The goal of this paper is to develop some new and useful tools for nonlinear analysis by applying the best approximation approach for classes of semiclosed 1-set contractive set-valued mappings in locally p-convex or p-vector spaces for In particular, we first develop general fixed point theorems for both set-valued and single-valued condensing mappings which provide answers to the Schauder conjecture in the affirmative way under the setting of (locally p-convex) p-vector spaces, then the best approximation results for upper semi-continuous and 1-set contractive set-valued are established, which are used as tools to establish some new fixed points for non-self set-valued mappings with either inward or outward set conditions under various situations. These results unify or improve corresponding results in the existing literature for nonlinear analysis.
{"title":"Fixed Point Theorem and Related Nonlinear Analysis by the Best Approximation Method in p-Vector Spaces","authors":"G. Yuan","doi":"10.1080/01630563.2023.2167088","DOIUrl":"https://doi.org/10.1080/01630563.2023.2167088","url":null,"abstract":"Abstract The goal of this paper is to develop some new and useful tools for nonlinear analysis by applying the best approximation approach for classes of semiclosed 1-set contractive set-valued mappings in locally p-convex or p-vector spaces for In particular, we first develop general fixed point theorems for both set-valued and single-valued condensing mappings which provide answers to the Schauder conjecture in the affirmative way under the setting of (locally p-convex) p-vector spaces, then the best approximation results for upper semi-continuous and 1-set contractive set-valued are established, which are used as tools to establish some new fixed points for non-self set-valued mappings with either inward or outward set conditions under various situations. These results unify or improve corresponding results in the existing literature for nonlinear analysis.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"221 - 295"},"PeriodicalIF":1.2,"publicationDate":"2023-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48522423","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 : 2023-01-20DOI: 10.1080/01630563.2022.2119248
Youness Alhabib Fajri
Abstract The aim of this article is twofold. First, we consider relatively monotone, relatively pseudomonotone, and relatively quasimonotone maps in nonsmooth setting. For continuous maps, we describe -monotonicity when the relative parameters are different and prove that -quasimonotonicity implies -quasimonotonicity as well as -pseudomonotonicity implies -pseudomonotonicity. Then, under local Lipschitzianity assumption, we establish first-order criteria for -monotonicity, -pseudomonotonicity, and -quasimonotonicity. Second, we introduce and study the new notion of relatively r-monotone operators. We provide characterizations and properties. We give in particular criteria of first order for relative r-monotonicity, in smooth and nonsmooth locally Lipschitz settings, when the relative parameters are equal.
{"title":"Relatively Monotone and Relatively Generalized Monotone Maps in Nonsmooth Setting and Relative r-Monotonicity","authors":"Youness Alhabib Fajri","doi":"10.1080/01630563.2022.2119248","DOIUrl":"https://doi.org/10.1080/01630563.2022.2119248","url":null,"abstract":"Abstract The aim of this article is twofold. First, we consider relatively monotone, relatively pseudomonotone, and relatively quasimonotone maps in nonsmooth setting. For continuous maps, we describe -monotonicity when the relative parameters are different and prove that -quasimonotonicity implies -quasimonotonicity as well as -pseudomonotonicity implies -pseudomonotonicity. Then, under local Lipschitzianity assumption, we establish first-order criteria for -monotonicity, -pseudomonotonicity, and -quasimonotonicity. Second, we introduce and study the new notion of relatively r-monotone operators. We provide characterizations and properties. We give in particular criteria of first order for relative r-monotonicity, in smooth and nonsmooth locally Lipschitz settings, when the relative parameters are equal.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"161 - 178"},"PeriodicalIF":1.2,"publicationDate":"2023-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45110094","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 : 2023-01-12DOI: 10.1080/01630563.2023.2166530
N. T. Chung, A. Ghanmi, T. Kenzizi
Abstract In this paper, we study the p-biharmonic equation of Kirchhoff type where is a positive parameter, is the p-Laplacian operator and is the p-biharmonic operator, V, K, g are nonnegative functions, V is vanishing at infinity in the sense that When the nonlinear term satisfies some suitable conditions, we prove that the above problem has at least two nontrivial solutions using the mountain pass theorem combined with the Ekeland variational principle.
{"title":"Multiple Solutions to p-Biharmonic Equations of Kirchhoff Type with Vanishing Potential","authors":"N. T. Chung, A. Ghanmi, T. Kenzizi","doi":"10.1080/01630563.2023.2166530","DOIUrl":"https://doi.org/10.1080/01630563.2023.2166530","url":null,"abstract":"Abstract In this paper, we study the p-biharmonic equation of Kirchhoff type where is a positive parameter, is the p-Laplacian operator and is the p-biharmonic operator, V, K, g are nonnegative functions, V is vanishing at infinity in the sense that When the nonlinear term satisfies some suitable conditions, we prove that the above problem has at least two nontrivial solutions using the mountain pass theorem combined with the Ekeland variational principle.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"202 - 220"},"PeriodicalIF":1.2,"publicationDate":"2023-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42803248","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 : 2023-01-06DOI: 10.1080/01630563.2022.2163503
A. Razani, G. Figueiredo
Abstract In this article, the degenerated horizontal (p, q)-Laplacian with weights and the competing horizontal (p, q)-Laplacian with weights including the Dirchlet boundary condition are studied. The existence and approximation results for these problems are studied where is a Carathéodory function, Ω is a bounded smooth domain in the Heisenberg group and stands for the horizontal p-Laplacian on The proofs are based on weighted Heisenberg Sobolev spaces, Nemytskij operators, Browder-Minty Theorem, and finite dimensional approximation.
{"title":"Degenerated and Competing Horizontal (p, q)-Laplacians with Weights on the Heisenberg Group","authors":"A. Razani, G. Figueiredo","doi":"10.1080/01630563.2022.2163503","DOIUrl":"https://doi.org/10.1080/01630563.2022.2163503","url":null,"abstract":"Abstract In this article, the degenerated horizontal (p, q)-Laplacian with weights and the competing horizontal (p, q)-Laplacian with weights including the Dirchlet boundary condition are studied. The existence and approximation results for these problems are studied where is a Carathéodory function, Ω is a bounded smooth domain in the Heisenberg group and stands for the horizontal p-Laplacian on The proofs are based on weighted Heisenberg Sobolev spaces, Nemytskij operators, Browder-Minty Theorem, and finite dimensional approximation.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"179 - 201"},"PeriodicalIF":1.2,"publicationDate":"2023-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42690383","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 : 2023-01-02DOI: 10.1080/01630563.2022.2163502
J. Balooee, Shih-sen Chang, Min Liu, Jinhua Zhu
Abstract The main purpose of this paper is to construct a new iterative algorithm using the notion of P-η-resolvent operator for solving a new system of generalized multi-valued variational-like inclusions in the setting of Banach spaces. As an application of the constructed algorithm, the strong convergence of the sequences generated by our proposed iterative algorithm to a solution of the system of generalized multi-valued variational-like inclusions is proved.
{"title":"Algorithmic Aspect and Iterative Approximation of a Solution for a System of Generalized Multi-Valued Variational-Like Inclusions in Banach Spaces","authors":"J. Balooee, Shih-sen Chang, Min Liu, Jinhua Zhu","doi":"10.1080/01630563.2022.2163502","DOIUrl":"https://doi.org/10.1080/01630563.2022.2163502","url":null,"abstract":"Abstract The main purpose of this paper is to construct a new iterative algorithm using the notion of P-η-resolvent operator for solving a new system of generalized multi-valued variational-like inclusions in the setting of Banach spaces. As an application of the constructed algorithm, the strong convergence of the sequences generated by our proposed iterative algorithm to a solution of the system of generalized multi-valued variational-like inclusions is proved.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"138 - 159"},"PeriodicalIF":1.2,"publicationDate":"2023-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45980569","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 : 2022-12-13DOI: 10.1080/01630563.2022.2153367
M. Mabdaoui, H. Moussa, M. Rhoudaf
Abstract In this paper, we shall study the polynomial approximation in a more general setting namely to consider the Orlicz-Sobolev spaces We study the local and global interpolation estimate and we will show the finite element error estimate for a nonlinear elliptic problem where we establish a generalization of Cea’s Theorem and we prove the modular convergence of the gradient, then we present the existence result and its proof.
{"title":"Variational Approximation in Modular Spaces by Using Finite Element Method Approach","authors":"M. Mabdaoui, H. Moussa, M. Rhoudaf","doi":"10.1080/01630563.2022.2153367","DOIUrl":"https://doi.org/10.1080/01630563.2022.2153367","url":null,"abstract":"Abstract In this paper, we shall study the polynomial approximation in a more general setting namely to consider the Orlicz-Sobolev spaces We study the local and global interpolation estimate and we will show the finite element error estimate for a nonlinear elliptic problem where we establish a generalization of Cea’s Theorem and we prove the modular convergence of the gradient, then we present the existence result and its proof.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"64 - 85"},"PeriodicalIF":1.2,"publicationDate":"2022-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43276145","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 : 2022-12-06DOI: 10.1080/01630563.2022.2150641
Na Zhang, Ji-jun Ao
Abstract In this paper, we mainly study the finite spectrum of Sturm–Liouville problems with transmission conditions dependent on the spectral parameter. By analyzing on the characteristic function, we prove that this kind of Sturm–Liouville problems consist of finite number of eigenvalue and these finite eigenvalues can be located anywhere in the complex plane. It is illustrated that the number of eigenvalues not only depends on the partition of the domain interval, but also depends on the transmission conditions dependent on the spectral parameter and the boundary conditions.
{"title":"Finite Spectrum of Sturm–Liouville Problems with Transmission Conditions Dependent on the Spectral Parameter","authors":"Na Zhang, Ji-jun Ao","doi":"10.1080/01630563.2022.2150641","DOIUrl":"https://doi.org/10.1080/01630563.2022.2150641","url":null,"abstract":"Abstract In this paper, we mainly study the finite spectrum of Sturm–Liouville problems with transmission conditions dependent on the spectral parameter. By analyzing on the characteristic function, we prove that this kind of Sturm–Liouville problems consist of finite number of eigenvalue and these finite eigenvalues can be located anywhere in the complex plane. It is illustrated that the number of eigenvalues not only depends on the partition of the domain interval, but also depends on the transmission conditions dependent on the spectral parameter and the boundary conditions.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"21 - 35"},"PeriodicalIF":1.2,"publicationDate":"2022-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44769234","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 : 2022-12-02DOI: 10.1080/01630563.2022.2150642
S. C. Buranay, M. A. Özarslan, S. S. Falahhesar
Abstract This research concerns some theoretical and numerical aspects of hybrid positive linear operators for approximating continuous functions on that have unbounded derivatives at the initial point. These operators are defined by using Modified Bernstein–Kantorovich operators where n is positive integer, is a fixed constant and reduces to the classical Bernstein–Kantorivich operators when To show the importance and the applicability of the given hybrid operators we develop an algorithm which implements them for solving the second kind linear Volterra integral equations with weakly singular kernels. Furthermore, applications are also performed on first kind integral equations, by utilizing regularization. Eventually, it is shown that the numerical realization of the given algorithm is easy and computationally efficient and gives accurate approximations to nonsmooth solutions.
{"title":"Hybrid Operators for Approximating Nonsmooth Functions and Applications on Volterra Integral Equations with Weakly Singular Kernels","authors":"S. C. Buranay, M. A. Özarslan, S. S. Falahhesar","doi":"10.1080/01630563.2022.2150642","DOIUrl":"https://doi.org/10.1080/01630563.2022.2150642","url":null,"abstract":"Abstract This research concerns some theoretical and numerical aspects of hybrid positive linear operators for approximating continuous functions on that have unbounded derivatives at the initial point. These operators are defined by using Modified Bernstein–Kantorovich operators where n is positive integer, is a fixed constant and reduces to the classical Bernstein–Kantorivich operators when To show the importance and the applicability of the given hybrid operators we develop an algorithm which implements them for solving the second kind linear Volterra integral equations with weakly singular kernels. Furthermore, applications are also performed on first kind integral equations, by utilizing regularization. Eventually, it is shown that the numerical realization of the given algorithm is easy and computationally efficient and gives accurate approximations to nonsmooth solutions.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"36 - 63"},"PeriodicalIF":1.2,"publicationDate":"2022-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43413022","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 : 2022-11-25DOI: 10.1080/01630563.2023.2221739
Hai Son Nguyen, T. Dao
Abstract The local stability of the solution map to a parametric boundary control problem governed by semilinear elliptic equations with finite mixed pointwise constraints is considered in this paper. We prove that the solution map is locally Hölder continuous in -norm of control variable when the strictly nonnegative second-order optimality conditions are satisfied for the unperturbed problem.
{"title":"Locally Hölder Continuity of the Solution Map to a Boundary Control Problem with Finite Mixed Control-State Constraints","authors":"Hai Son Nguyen, T. Dao","doi":"10.1080/01630563.2023.2221739","DOIUrl":"https://doi.org/10.1080/01630563.2023.2221739","url":null,"abstract":"Abstract The local stability of the solution map to a parametric boundary control problem governed by semilinear elliptic equations with finite mixed pointwise constraints is considered in this paper. We prove that the solution map is locally Hölder continuous in -norm of control variable when the strictly nonnegative second-order optimality conditions are satisfied for the unperturbed problem.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"987 - 1011"},"PeriodicalIF":1.2,"publicationDate":"2022-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46031860","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 : 2022-11-08DOI: 10.1080/01630563.2022.2141254
M. H. Geoffroy, James Larrouy
Abstract In this paper, we introduce a topology on the power set of a partially ordered normed space Z from which we derive a topological convergence on along with new concepts of continuity and semicontinuity for set-valued mappings. Our goal is to propose an appropriate framework to address set optimization problems involving set relations based on a cone ordering. Taking advantage of this new setting, we establish several results regarding the well-posedness of set-valued optimization problems that are consistent with the state-of-the-art.
{"title":"A New Topological Framework and Its Application to Well-Posedness in Set-Valued Optimization","authors":"M. H. Geoffroy, James Larrouy","doi":"10.1080/01630563.2022.2141254","DOIUrl":"https://doi.org/10.1080/01630563.2022.2141254","url":null,"abstract":"Abstract In this paper, we introduce a topology on the power set of a partially ordered normed space Z from which we derive a topological convergence on along with new concepts of continuity and semicontinuity for set-valued mappings. Our goal is to propose an appropriate framework to address set optimization problems involving set relations based on a cone ordering. Taking advantage of this new setting, we establish several results regarding the well-posedness of set-valued optimization problems that are consistent with the state-of-the-art.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"43 1","pages":"1848 - 1883"},"PeriodicalIF":1.2,"publicationDate":"2022-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42897605","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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