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Core–EP Star and Star Core–EP Operators Core–EP Star和Star Core–EP运营商
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2023-04-05 DOI: 10.1080/01630563.2023.2197991
Katarina S. Stojanović
{"title":"Core–EP Star and Star Core–EP Operators","authors":"Katarina S. Stojanović","doi":"10.1080/01630563.2023.2197991","DOIUrl":"https://doi.org/10.1080/01630563.2023.2197991","url":null,"abstract":"Abstract In this paper, we will introduce two new classes of generalized Drazin invertible operators on Hilbert space, which are called core–EP star and star core–EP operators, using the core–EP inverse and the adjoint of a given operator. We also represent here a few characterizations of these new operators from two points of view, algebraic and geometrical, and make relations to some familiar inverses, which are studied before. Next, we will consider two decompositions of Hilbert space and give the matrix representations of these new operators, following the decompositions. As the special section, there is the case when the operator is Drazin invertible. By using a *core–EP inverse, instead of the core–EP inverse, we get another new classes called *core–EP star and star *core–EP operators.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45083825","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
Accuracy Estimates for Bilinear Optimal Control Problems Governed by Ordinary Differential Equations 常微分方程双线性最优控制问题的精度估计
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2023-03-31 DOI: 10.1080/01630563.2023.2192776
Jacob Körner, A. Borzì
{"title":"Accuracy Estimates for Bilinear Optimal Control Problems Governed by Ordinary Differential Equations","authors":"Jacob Körner, A. Borzì","doi":"10.1080/01630563.2023.2192776","DOIUrl":"https://doi.org/10.1080/01630563.2023.2192776","url":null,"abstract":"Abstract First- and second-order accuracy estimates for an optimal control problem governed by a system of ordinary differential equations with a bilinear control mechanism are presented. The numerical time discretization scheme under consideration is the finite element method with continuous piecewise linear functions. Central to this work is a first- and second-order analysis of optimality of the continuous and approximated optimal control problems. In the case of box constraints on the control, first-order error estimates for the control function are obtained assuming a piecewise constant approximation of the control, whereas second-order accuracy can be obtained in the case of a continuous, piecewise polynomial approximation. Numerical evidence is presented that supports the theoretical findings.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47612458","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
λ-Bernstein Operators Based on Pólya Distribution 基于Pólya分布的λ-Bernstein算子
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2023-03-16 DOI: 10.1080/01630563.2023.2185896
Km. Lipi, N. Deo
{"title":"λ-Bernstein Operators Based on Pólya Distribution","authors":"Km. Lipi, N. Deo","doi":"10.1080/01630563.2023.2185896","DOIUrl":"https://doi.org/10.1080/01630563.2023.2185896","url":null,"abstract":"Abstract In this manuscript, we propose a Pólya distribution-based generalization of -Bernstein operators. We establish some fundamental results for convergence as well as order of approximation of the proposed operators. We present theoretical result and graph to demonstrate the proposed operator’s intriguing ability to interpolate at the interval’s end points. In order to illustrate the convergence of proposed operators as well as the effect of changing the parameter “ ” we provide a variety of results and graphs as our paper’s conclusion.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45620370","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 Note on Stability of Parabolic Difference Equations on Torus 关于Torus上抛物型差分方程稳定性的一个注记
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2023-03-03 DOI: 10.1080/01630563.2023.2183509
A. Ashyralyev, F. Hezenci, Y. Sozen
{"title":"A Note on Stability of Parabolic Difference Equations on Torus","authors":"A. Ashyralyev, F. Hezenci, Y. Sozen","doi":"10.1080/01630563.2023.2183509","DOIUrl":"https://doi.org/10.1080/01630563.2023.2183509","url":null,"abstract":"Abstract The present article investigates nonlocal boundary value problems for parabolic equations of reverse type on torus. The first order of accuracy difference scheme for the numerical solution of nonlocal boundary value problems for parabolic equations on circle and torus are presented. For the solutions of the difference scheme, the stability estimates and coercivity estimates in various Hölder norms are established. Furthermore, theoretical results are supported by numerical experiments.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43085847","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
Applications of Fell Topology to Closed Set-Valued Optimizations in Partially Ordered First Countable Topological Vector Spaces 倒拓扑在部分有序第一可数拓扑向量空间闭集值优化中的应用
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2023-03-03 DOI: 10.1080/01630563.2023.2180753
Jinlu Li
{"title":"Applications of Fell Topology to Closed Set-Valued Optimizations in Partially Ordered First Countable Topological Vector Spaces","authors":"Jinlu Li","doi":"10.1080/01630563.2023.2180753","DOIUrl":"https://doi.org/10.1080/01630563.2023.2180753","url":null,"abstract":"Abstract Let (X, ) be a topological vector space equipped with a partial order which is induced by a nonempty pointed closed and convex cone K in X. Let (X) = 2 X be the power set of X and (X) = 2 X { }. In this paper, we consider the so called upward preordering on (X), which has been used by many authors (see [4 7, 9, 11 14, 18 19]). We first prove some properties of this ordering relation Let (X) denote the collection of all -closed subsets of X and (X) = (X){ }, which is equipped with the Fell topology Let C be a nonempty subset of X and let F: C (X) be a closed set-valued mapping. By applying the Fell topology on (X) and the Fan-KKM Theorem, we prove some existence theorems for some -minimization and -maximization problems with respect to F subject to the subset C for first countable topological vector spaces. These results will be applied to solve some closed ball-valued optimization problems in partially ordered Hilbert spaces. Some examples will be provided in","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44599902","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
Q-duals and Q-approximate duals of g-frames in Hilbert spaces Hilbert空间中g坐标系的q -对偶和q -近似对偶
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2023-02-27 DOI: 10.1080/01630563.2023.2184383
Xiangchun Xiao, G. Zhao, Guorong Zhou
{"title":"Q-duals and Q-approximate duals of g-frames in Hilbert spaces","authors":"Xiangchun Xiao, G. Zhao, Guorong Zhou","doi":"10.1080/01630563.2023.2184383","DOIUrl":"https://doi.org/10.1080/01630563.2023.2184383","url":null,"abstract":"Abstract In this paper we mainly discuss the properties of Q-duals and Q-approximate duals of g-frames in Hilbert spaces. Given and being a pair of Q-dual, being some kind of perturbed sequence of in general is not a Q-approximate dual of We then give four different kinds of perturbed conditions such that and a perturbed sequence of are possible to be a pair of Q-approximate dual. We also provide several different methods to construct Q-duals and Q-approximate duals of g-frames. Finally, we give two equivalent characterizations of Q-duals and Q-approximate duals by using the associated induced sequences.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44453479","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 Variational and Regularization Framework for Stable Strong Solutions of Nonlinear Boundary Value Problems 一类非线性边值问题稳定强解的变分正则化框架
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2023-02-23 DOI: 10.1080/01630563.2023.2178010
J. Jerome
{"title":"A Variational and Regularization Framework for Stable Strong Solutions of Nonlinear Boundary Value Problems","authors":"J. Jerome","doi":"10.1080/01630563.2023.2178010","DOIUrl":"https://doi.org/10.1080/01630563.2023.2178010","url":null,"abstract":"Abstract We study a variational approach introduced by S.D. Fisher and the author in the 1970s in the context of norm minimization for differentiable mappings occurring in nonlinear elliptic boundary value problems. It may be viewed as an abstract version of the calculus of variations. A strong hypothesis, initially limiting the scope of this approach, is the assumption of a bounded minimizing sequence in the least squares formulation. In this article, we employ regularization and invariant regions to overcome this obstacle. A consequence of the framework is the convergence of approximations for regularized problems to a desired solution. The variational method is closely associated with the implicit function theorem, and it can be jointly studied, so that continuous parameter stability is naturally deduced. A significant aspect of the theory is that the reaction term in a reaction-diffusion equation can be selected to act globally as in the steady Schrödinger-Hartree equation. Local action, as in the non-equilibrium Poisson-Boltzmann equation, is also included. Both cases are studied at length prior to the development of a general theory.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42139912","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
Optimal Control Results for Sobolev-Type Fractional Stochastic Volterra-Fredholm Integrodifferential Systems of Order ϑ ∈ (1, 2) via Sectorial Operators Sobolev型分数阶随机Volterra—Fredholm积分微分系统的最优控制结果 ∈ （1， 2） 通过行业运营商
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2023-02-22 DOI: 10.1080/01630563.2023.2180645
M. Johnson, V. Vijayakumar
{"title":"Optimal Control Results for Sobolev-Type Fractional Stochastic Volterra-Fredholm Integrodifferential Systems of Order ϑ ∈ (1, 2) via Sectorial Operators","authors":"M. Johnson, V. Vijayakumar","doi":"10.1080/01630563.2023.2180645","DOIUrl":"https://doi.org/10.1080/01630563.2023.2180645","url":null,"abstract":"Abstract The objective of this paper is to investigate the optimal control results for Sobolev-type fractional stochastic Volterra-Fredholm integrodifferential systems of order with sectorial operators in Hilbert spaces. Initially, we prove the existence of mild solutions by using fractional calculus, stochastic analysis theory, and the Schauder’s fixed point theorem. Next, we demonstrate the existence of optimal control pairs for the given system. Finally, an example is included to show the applications of the developed theory.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49104198","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: 5
Regional Boundary Observability for Semilinear Fractional Systems with Riemann-Liouville Derivative 具有Riemann-Liouville导数的半线性分数阶系统的区域边界可观测性
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2023-02-15 DOI: 10.1080/01630563.2023.2171055
Khalid Zguaid, F. E. El Alaoui
{"title":"Regional Boundary Observability for Semilinear Fractional Systems with Riemann-Liouville Derivative","authors":"Khalid Zguaid, F. E. El Alaoui","doi":"10.1080/01630563.2023.2171055","DOIUrl":"https://doi.org/10.1080/01630563.2023.2171055","url":null,"abstract":"Abstract In this manuscript, we consider the problem of regional boundary observability for semilinear time-fractional systems involving the Riemann-Liouville fractional derivative. Our primary goal is to focus on reconstructing the initial state in the desired subregion located on the boundary of the spatial domain. To do that, we firstly construct a link between regional boundary observability of the considered semilinear system and regional observability of its linear part. And with the help of an extension of the Hilbert uniqueness method (HUM), we recover the value of the initial state on the desired boundary subregion. We also provide a numerical simulation based on the steps of the HUM approach that shows the proposed algorithm’s efficiency and backs up our theoretical results.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42685302","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
On Some Inequalities of Differentiable Uniformly Convex Mapping with Applications 关于可微一致凸映射的一些不等式及其应用
IF 1.2 4区 数学
Numerical Functional Analysis and Optimization Pub Date : 2023-02-06 DOI: 10.1080/01630563.2023.2174989
H. Barsam, Y. Sayyari
{"title":"On Some Inequalities of Differentiable Uniformly Convex Mapping with Applications","authors":"H. Barsam, Y. Sayyari","doi":"10.1080/01630563.2023.2174989","DOIUrl":"https://doi.org/10.1080/01630563.2023.2174989","url":null,"abstract":"Abstract The widely known hermite-hadamard-Fejer type inequalities are so important in the field of mathematical analysis. Many researchers have studied on these inequalities. In this paper, we have obtained several inequalities related to the Hermite-Hadamard inequality for a special class of the functions called uniformly convex functions. We have also presented applications of these obtained inequalities in some error estimates for higher moments of random variables.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46695400","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
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