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Finite Spectrum of Sturm–Liouville Problems with Transmission Conditions Dependent on the Spectral Parameter 传输条件依赖于谱参数的Sturm-Liouville问题的有限谱
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2022-12-06 DOI: 10.1080/01630563.2022.2150641
Na Zhang, Ji-jun Ao
{"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":null,"pages":null},"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}
引用次数: 1
Hybrid Operators for Approximating Nonsmooth Functions and Applications on Volterra Integral Equations with Weakly Singular Kernels 近似非光滑函数的混合算子及其在弱奇异核Volterra积分方程上的应用
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2022-12-02 DOI: 10.1080/01630563.2022.2150642
S. C. Buranay, M. A. Özarslan, S. S. Falahhesar
{"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":null,"pages":null},"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}
引用次数: 2
Locally Hölder Continuity of the Solution Map to a Boundary Control Problem with Finite Mixed Control-State Constraints 有限混合控制状态约束边界控制问题解映射的局部Hölder连续性
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2022-11-25 DOI: 10.1080/01630563.2023.2221739
Hai Son Nguyen, T. Dao
{"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":null,"pages":null},"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}
引用次数: 0
A New Topological Framework and Its Application to Well-Posedness in Set-Valued Optimization 一种新的拓扑框架及其在集值优化的适定性中的应用
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2022-11-08 DOI: 10.1080/01630563.2022.2141254
M. H. Geoffroy, James Larrouy
{"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":null,"pages":null},"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}
引用次数: 0
Fixed Point Theorems for Operators with Certain Condition in p-Uniformly Convex Metric Spaces p-一致凸度量空间中具有一定条件的算子的不动点定理
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2022-11-04 DOI: 10.1080/01630563.2022.2141256
Mohammad Knefati, V. Karakaya
{"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":null,"pages":null},"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}
引用次数: 0
Generalized Drazin Invertibility of Operator Matrices 算子矩阵的广义Drazin可逆性
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2022-10-28 DOI: 10.1080/01630563.2022.2137811
Aymen Bahloul, I. Walha
{"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":null,"pages":null},"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}
引用次数: 1
On the Eigenstructure of the Modified Bernstein Operators 关于修正Bernstein算子的特征结构
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2022-10-28 DOI: 10.1080/01630563.2022.2136695
Övgü Gürel Yılmaz, Sofiya Ostrovska, M. Turan
{"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":null,"pages":null},"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}
引用次数: 0
Properties of the Solution Set of a Class of Mixed Variational Inqualities 一类混合变分不等式解集的性质
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2022-10-21 DOI: 10.1080/01630563.2022.2135102
Yang Xu, Zhenghai Huang
{"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":null,"pages":null},"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}
引用次数: 0
Phase Retrieval from Linear Canonical Transforms 基于线性正则变换的相位检索
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2022-10-19 DOI: 10.1080/01630563.2022.2132511
Yang Chen, Na Qu
{"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":null,"pages":null},"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}
引用次数: 1
Combined Legendre Spectral-Finite Element Methods for Two-Dimensional Fredholm Integral Equations of the Second Kind 二维第二类Fredholm积分方程的联合Legendre谱-有限元方法
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2022-10-19 DOI: 10.1080/01630563.2022.2135540
B. L. Panigrahi
{"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":null,"pages":null},"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}
引用次数: 0
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