Pub Date : 2022-11-04DOI: 10.1080/01630563.2022.2141256
Mohammad Knefati, V. Karakaya
Abstract In this paper, firstly, we extend the nonlinear Lebesgue spaces from the setting of Hadamard spaces to the setting of p-uniformly convex metric spaces. Afterward, we establish some Δ-convergence and strong convergence theorems for a recently introduced class of generalized nonexpansive mappings in the setting of p-uniformly convex metric spaces. Furthermore, we employ the newly introduced JK-iteration process to approximate the fixed points of this class. Finally, we construct new examples of this class of mappings in the context of p-uniformly convex metric spaces.
{"title":"Fixed Point Theorems for Operators with Certain Condition in p-Uniformly Convex Metric Spaces","authors":"Mohammad Knefati, V. Karakaya","doi":"10.1080/01630563.2022.2141256","DOIUrl":"https://doi.org/10.1080/01630563.2022.2141256","url":null,"abstract":"Abstract In this paper, firstly, we extend the nonlinear Lebesgue spaces from the setting of Hadamard spaces to the setting of p-uniformly convex metric spaces. Afterward, we establish some Δ-convergence and strong convergence theorems for a recently introduced class of generalized nonexpansive mappings in the setting of p-uniformly convex metric spaces. Furthermore, we employ the newly introduced JK-iteration process to approximate the fixed points of this class. Finally, we construct new examples of this class of mappings in the context of p-uniformly convex metric spaces.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"43 1","pages":"1884 - 1900"},"PeriodicalIF":1.2,"publicationDate":"2022-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49362857","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 : 2022-10-28DOI: 10.1080/01630563.2022.2137811
Aymen Bahloul, I. Walha
Abstract In this paper, we investigate the generalized Drazin invertibility of upper triangular operator matrices acting on Banach spaces. Among other things, we explicit the defect set with respect to the local spectral theory. Moreover, we exhibit some sufficient conditions which assure that the generalized Drazin spectrum of a 3 × 3 upper triangular block operator matrix is the union of its diagonal entries spectra.
{"title":"Generalized Drazin Invertibility of Operator Matrices","authors":"Aymen Bahloul, I. Walha","doi":"10.1080/01630563.2022.2137811","DOIUrl":"https://doi.org/10.1080/01630563.2022.2137811","url":null,"abstract":"Abstract In this paper, we investigate the generalized Drazin invertibility of upper triangular operator matrices acting on Banach spaces. Among other things, we explicit the defect set with respect to the local spectral theory. Moreover, we exhibit some sufficient conditions which assure that the generalized Drazin spectrum of a 3 × 3 upper triangular block operator matrix is the union of its diagonal entries spectra.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"43 1","pages":"1836 - 1847"},"PeriodicalIF":1.2,"publicationDate":"2022-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49431605","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 : 2022-10-28DOI: 10.1080/01630563.2022.2136695
Övgü Gürel Yılmaz, Sofiya Ostrovska, M. Turan
Abstract Starting from the well-known work of Cooper and Waldron published in 2000, the eigenstructure of various Bernstein-type operators has been investigated by many researchers. In this work, the eigenvalues and eigenvectors of the modified Bernstein operators Qn have been studied. These operators were introduced by S. N. Bernstein himself, in 1932, for the purpose of accelerating the approximation rate for smooth functions. Here, the explicit formulae for the eigenvalues and corresponding eigenpolynomials together with their limiting behavior are established. The results show that although some outcomes are similar to those for the Bernstein operators, there are essentially different ones as well.
{"title":"On the Eigenstructure of the Modified Bernstein Operators","authors":"Övgü Gürel Yılmaz, Sofiya Ostrovska, M. Turan","doi":"10.1080/01630563.2022.2136695","DOIUrl":"https://doi.org/10.1080/01630563.2022.2136695","url":null,"abstract":"Abstract Starting from the well-known work of Cooper and Waldron published in 2000, the eigenstructure of various Bernstein-type operators has been investigated by many researchers. In this work, the eigenvalues and eigenvectors of the modified Bernstein operators Qn have been studied. These operators were introduced by S. N. Bernstein himself, in 1932, for the purpose of accelerating the approximation rate for smooth functions. Here, the explicit formulae for the eigenvalues and corresponding eigenpolynomials together with their limiting behavior are established. The results show that although some outcomes are similar to those for the Bernstein operators, there are essentially different ones as well.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"43 1","pages":"1821 - 1835"},"PeriodicalIF":1.2,"publicationDate":"2022-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44924578","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 : 2022-10-21DOI: 10.1080/01630563.2022.2135102
Yang Xu, Zhenghai Huang
Abstract In this paper, we investigate a class of mixed variational inequalities on nonempty closed convex subsets of real Euclidean spaces. One of the mappings involved is lower semicontinuous and the other is weakly homogeneous. After discussing the boundedness for the solution set (if it is nonempty) of the problem, we focus on the nonemptiness and compactness of the solution set. Two new results on the nonemptiness and compactness of the solution set of the problem are established, and some examples are used to compare the results with those in the literature. It can be seen that new results improve some known related results.
{"title":"Properties of the Solution Set of a Class of Mixed Variational Inqualities","authors":"Yang Xu, Zhenghai Huang","doi":"10.1080/01630563.2022.2135102","DOIUrl":"https://doi.org/10.1080/01630563.2022.2135102","url":null,"abstract":"Abstract In this paper, we investigate a class of mixed variational inequalities on nonempty closed convex subsets of real Euclidean spaces. One of the mappings involved is lower semicontinuous and the other is weakly homogeneous. After discussing the boundedness for the solution set (if it is nonempty) of the problem, we focus on the nonemptiness and compactness of the solution set. Two new results on the nonemptiness and compactness of the solution set of the problem are established, and some examples are used to compare the results with those in the literature. It can be seen that new results improve some known related results.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"43 1","pages":"1779 - 1800"},"PeriodicalIF":1.2,"publicationDate":"2022-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49360770","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 : 2022-10-19DOI: 10.1080/01630563.2022.2132511
Yang Chen, Na Qu
Abstract The classical phase retrieval problem aims to recover an unknown function from the Fourier magnitudes. The linear canonical transform has a more generalized form of the well-known (fractional) Fourier transform and a wide range of engineering applications such as optics and quantum mechanism. In this paper, we consider the linear canonic phase retrieval problem of determining a function from the magnitudes of the linear canonic transforms. We show that a compactly supported function f can be determined, up to a global phase, from the magnitudes of multiple linear canonic transforms, where is a class of real unimodular matrices. It generalizes the results of phase retrieval from multiple fractional Fourier transforms. On the other hand, we show that a compactly supported function f can be determined, up to a global phase, from the interference linear canonic magnitudes and where Moreover, if the ambiguity of conjugate reflection is taken into account, the compactly supported function f can be determined, up to a rotation and conjugate reflection, from the linear canonic magnitudes and
{"title":"Phase Retrieval from Linear Canonical Transforms","authors":"Yang Chen, Na Qu","doi":"10.1080/01630563.2022.2132511","DOIUrl":"https://doi.org/10.1080/01630563.2022.2132511","url":null,"abstract":"Abstract The classical phase retrieval problem aims to recover an unknown function from the Fourier magnitudes. The linear canonical transform has a more generalized form of the well-known (fractional) Fourier transform and a wide range of engineering applications such as optics and quantum mechanism. In this paper, we consider the linear canonic phase retrieval problem of determining a function from the magnitudes of the linear canonic transforms. We show that a compactly supported function f can be determined, up to a global phase, from the magnitudes of multiple linear canonic transforms, where is a class of real unimodular matrices. It generalizes the results of phase retrieval from multiple fractional Fourier transforms. On the other hand, we show that a compactly supported function f can be determined, up to a global phase, from the interference linear canonic magnitudes and where Moreover, if the ambiguity of conjugate reflection is taken into account, the compactly supported function f can be determined, up to a rotation and conjugate reflection, from the linear canonic magnitudes and","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"43 1","pages":"1760 - 1777"},"PeriodicalIF":1.2,"publicationDate":"2022-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43273783","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 : 2022-10-19DOI: 10.1080/01630563.2022.2135540
B. L. Panigrahi
Abstract In this paper, we will discuss on the Combined Legendre spectral-Finite element methods (CLSFEM) for the two-dimensional Fredholm integral equations with smooth kernel on the Banach spaces and the corresponding eigenvalue problem. In these methods, the approximated finite dimensional space is the cartesian product of spline space and Legendre polynomial space. The problem is approximated by the CLSFEM using orthogonal projection, which projects from the Banach space into the finite dimensional space. The convergence analysis for both Fredholm integral equations and the corresponding eigenvalue problem will be discussed in both L 2 and norms. The numerical results will be shown to validate the theoretical estimate.
{"title":"Combined Legendre Spectral-Finite Element Methods for Two-Dimensional Fredholm Integral Equations of the Second Kind","authors":"B. L. Panigrahi","doi":"10.1080/01630563.2022.2135540","DOIUrl":"https://doi.org/10.1080/01630563.2022.2135540","url":null,"abstract":"Abstract In this paper, we will discuss on the Combined Legendre spectral-Finite element methods (CLSFEM) for the two-dimensional Fredholm integral equations with smooth kernel on the Banach spaces and the corresponding eigenvalue problem. In these methods, the approximated finite dimensional space is the cartesian product of spline space and Legendre polynomial space. The problem is approximated by the CLSFEM using orthogonal projection, which projects from the Banach space into the finite dimensional space. The convergence analysis for both Fredholm integral equations and the corresponding eigenvalue problem will be discussed in both L 2 and norms. The numerical results will be shown to validate the theoretical estimate.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"43 1","pages":"1801 - 1820"},"PeriodicalIF":1.2,"publicationDate":"2022-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48584640","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 : 2022-10-17DOI: 10.1080/01630563.2022.2132510
T. Su, D. Luu
Abstract In this article, some types of lower and upper second-order strictly pseudoconvexity are provided for establishing sufficient conditions for the second-order strict local Pareto minima of nonsmooth vector equilibrium problem with set, inequality and equality constraints. Based on the notion of Gerstewitz mappings, some Kuhn-Tucker-type multiplier rules for the strict local Pareto minima of such problem are obtained. We also construct the second-order constraint qualification in terms of first- and second-order directional derivatives of the (CQ) and (CQ1) types. Using this constraint qualifications, some second-order primal and dual necessary optimality conditions in terms of second-order upper and lower Dini directional derivatives for such minima are derived. Under suitable assumptions on the lower and upper strictly pseudoconvexity of order two of objective and constraint functions, second-order necessary optimality conditions become sufficient optimality conditions to such problem. Some illustrative examples are also given for our findings.
{"title":"Second-Order Optimality Conditions for Strict Pareto Minima and Weak Efficiency for Nonsmooth Constrained Vector Equilibrium Problems","authors":"T. Su, D. Luu","doi":"10.1080/01630563.2022.2132510","DOIUrl":"https://doi.org/10.1080/01630563.2022.2132510","url":null,"abstract":"Abstract In this article, some types of lower and upper second-order strictly pseudoconvexity are provided for establishing sufficient conditions for the second-order strict local Pareto minima of nonsmooth vector equilibrium problem with set, inequality and equality constraints. Based on the notion of Gerstewitz mappings, some Kuhn-Tucker-type multiplier rules for the strict local Pareto minima of such problem are obtained. We also construct the second-order constraint qualification in terms of first- and second-order directional derivatives of the (CQ) and (CQ1) types. Using this constraint qualifications, some second-order primal and dual necessary optimality conditions in terms of second-order upper and lower Dini directional derivatives for such minima are derived. Under suitable assumptions on the lower and upper strictly pseudoconvexity of order two of objective and constraint functions, second-order necessary optimality conditions become sufficient optimality conditions to such problem. Some illustrative examples are also given for our findings.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"43 1","pages":"1732 - 1759"},"PeriodicalIF":1.2,"publicationDate":"2022-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44367351","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 : 2022-09-27DOI: 10.1080/01630563.2022.2124271
B. T. Kien, N. Tuan
Abstract This paper gives some sufficient conditions for convergence of approximate solutions to seminlinear elliptic optimal control problems with mixed pointwise constraints. We build discrete optimal control problems by the finite element method in type of the full control discretization. We show that if the strictly second-order sufficient condition is valid, then some error estimates between approximate solutions of discrete optimal control problems and optimal solutions of the original problem are obtained.
{"title":"Error Estimates for Approximate Solutions to Seminlinear Elliptic Optimal Control Problems with Nonlinear and Mixed Constraints","authors":"B. T. Kien, N. Tuan","doi":"10.1080/01630563.2022.2124271","DOIUrl":"https://doi.org/10.1080/01630563.2022.2124271","url":null,"abstract":"Abstract This paper gives some sufficient conditions for convergence of approximate solutions to seminlinear elliptic optimal control problems with mixed pointwise constraints. We build discrete optimal control problems by the finite element method in type of the full control discretization. We show that if the strictly second-order sufficient condition is valid, then some error estimates between approximate solutions of discrete optimal control problems and optimal solutions of the original problem are obtained.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"43 1","pages":"1672 - 1706"},"PeriodicalIF":1.2,"publicationDate":"2022-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49187155","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 : 2022-09-24DOI: 10.1080/01630563.2022.2124270
M. A. Hasankhani Fard
Abstract It is constructed infinite frames with some given redundancy. In this paper, the solution of the construction problem of infinite frames with given redundancy, is completed. More precisely, all possible infinite frame redundancies are characterized.
{"title":"The Complete Solution of the Construction Problem of Infinite Frames with Given Redundancy","authors":"M. A. Hasankhani Fard","doi":"10.1080/01630563.2022.2124270","DOIUrl":"https://doi.org/10.1080/01630563.2022.2124270","url":null,"abstract":"Abstract It is constructed infinite frames with some given redundancy. In this paper, the solution of the construction problem of infinite frames with given redundancy, is completed. More precisely, all possible infinite frame redundancies are characterized.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"43 1","pages":"1660 - 1671"},"PeriodicalIF":1.2,"publicationDate":"2022-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42282865","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 : 2022-09-21DOI: 10.1080/01630563.2022.2123818
N. Hazzam, Z. Kebbiche
Abstract In this article, a new variant of Mehrotra type-predictor-corrector algorithm is proposed for -horizontal linear complementarity problem. We demonstrate the theoretical efficiency of this algorithm by showing its polynomial complexity. The iteration bound is given by We test the practical efficiency and the validity of our algorithm by running some computational tests.
{"title":"A Mehrotra Type Predictor-Corrector Interior-Point Method for -HLCP","authors":"N. Hazzam, Z. Kebbiche","doi":"10.1080/01630563.2022.2123818","DOIUrl":"https://doi.org/10.1080/01630563.2022.2123818","url":null,"abstract":"Abstract In this article, a new variant of Mehrotra type-predictor-corrector algorithm is proposed for -horizontal linear complementarity problem. We demonstrate the theoretical efficiency of this algorithm by showing its polynomial complexity. The iteration bound is given by We test the practical efficiency and the validity of our algorithm by running some computational tests.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"43 1","pages":"1647 - 1659"},"PeriodicalIF":1.2,"publicationDate":"2022-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42389841","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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