Pub Date : 2023-03-03DOI: 10.1080/01630563.2023.2183509
A. Ashyralyev, F. Hezenci, Y. Sozen
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.
{"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":"44 1","pages":"490 - 509"},"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}
Pub Date : 2023-02-27DOI: 10.1080/01630563.2023.2184383
Xiangchun Xiao, G. Zhao, Guorong Zhou
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.
{"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":"44 1","pages":"510 - 528"},"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}
Pub Date : 2023-02-23DOI: 10.1080/01630563.2023.2178010
J. Jerome
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.
{"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":"44 1","pages":"394 - 419"},"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}
Pub Date : 2023-02-22DOI: 10.1080/01630563.2023.2180645
M. Johnson, V. Vijayakumar
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.
{"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":"44 1","pages":"439 - 460"},"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}
Pub Date : 2023-02-15DOI: 10.1080/01630563.2023.2171055
Khalid Zguaid, F. E. El Alaoui
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.
{"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":"44 1","pages":"420 - 437"},"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}
Pub Date : 2023-02-06DOI: 10.1080/01630563.2023.2174989
H. Barsam, Y. Sayyari
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.
{"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":"44 1","pages":"368 - 381"},"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}
{"title":"Further Hilbert-Schmidt Numerical Radius Inequalities for 2 × 2 Operator Matrices","authors":"Soumia Aici, Abdelkader Frakis, Fuad Kittaneh","doi":"10.1080/01630563.2023.2174990","DOIUrl":"https://doi.org/10.1080/01630563.2023.2174990","url":null,"abstract":"We give several bounds for the Hilbert-Schmidt numerical radii of 2 × 2 operator matrices. Some of these bounds are refinements of the existing ones.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135006673","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 : 2023-02-01DOI: 10.1080/01630563.2023.2172033
Bilel Krichen, B. Mefteh, Rahma Taktak
Abstract The purpose of this paper is to extend Boyd and Wong’s fixed point theorem in complete generalized metric spaces and to apply this result under the so-called G-weak topology in generalized Banach algebras. Some tools will be introduced and involved in our work as the generalized measures of weak non-compactness and the sequential condition Our results will extend many known theorems in the literature. Also, we will give an application for an infinite system of nonlinear integral equations defined on the generalized Banach algebra where c 0 is the space of all real sequences converging to zero.
{"title":"Fixed Point Theorems in Generalized Banach Algebras and an Application to Infinite Systems in 𝒞([0, 1], c 0) × 𝒞([0, 1], c 0)","authors":"Bilel Krichen, B. Mefteh, Rahma Taktak","doi":"10.1080/01630563.2023.2172033","DOIUrl":"https://doi.org/10.1080/01630563.2023.2172033","url":null,"abstract":"Abstract The purpose of this paper is to extend Boyd and Wong’s fixed point theorem in complete generalized metric spaces and to apply this result under the so-called G-weak topology in generalized Banach algebras. Some tools will be introduced and involved in our work as the generalized measures of weak non-compactness and the sequential condition Our results will extend many known theorems in the literature. Also, we will give an application for an infinite system of nonlinear integral equations defined on the generalized Banach algebra where c 0 is the space of all real sequences converging to zero.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"333 - 367"},"PeriodicalIF":1.2,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44124331","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 : 2023-02-01DOI: 10.1080/01630563.2023.2171053
Jia Li, Xiaoling Hao, Kun Li, Siqin Yao
Abstract For any positive integer 2n and any positive integer m, l, a class of regular self-adjoint and non-self-adjoint boundary value problems whose spectrum consists of at most eigenvalues is constructed. The key to this analysis is the division of intervals and an iterative construction of the characteristic function. In the self-adjoint case with separated boundary conditions this upper bound can be improved to
{"title":"Finite Spectrum of 2nth Order Boundary Value Problems with Transmission Conditions","authors":"Jia Li, Xiaoling Hao, Kun Li, Siqin Yao","doi":"10.1080/01630563.2023.2171053","DOIUrl":"https://doi.org/10.1080/01630563.2023.2171053","url":null,"abstract":"Abstract For any positive integer 2n and any positive integer m, l, a class of regular self-adjoint and non-self-adjoint boundary value problems whose spectrum consists of at most eigenvalues is constructed. The key to this analysis is the division of intervals and an iterative construction of the characteristic function. In the self-adjoint case with separated boundary conditions this upper bound can be improved to","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"296 - 310"},"PeriodicalIF":1.2,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48706900","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 : 2023-01-28DOI: 10.1080/01630563.2023.2171054
Qingyue Zhang, Zhen Guo, Bei Liu, Rui Li
Abstract In the article, we consider the problem of phase retrieval from magnitudes of STFT (short-time Fourier transform) measurements. The uniqueness of STFT phase retrieval had been established when the signal is one-dimensional function. In this article, we investigate the uniqueness of STFT phase retrieval when the signal is a two-dimensional vector function. And we prove the uniqueness theorem of STFT phase retrieval for bandlimited real-valued and complex-valued vector functions, respectively.
{"title":"Uniqueness of STFT Phase Retrieval for Bandlimited Vector Functions","authors":"Qingyue Zhang, Zhen Guo, Bei Liu, Rui Li","doi":"10.1080/01630563.2023.2171054","DOIUrl":"https://doi.org/10.1080/01630563.2023.2171054","url":null,"abstract":"Abstract In the article, we consider the problem of phase retrieval from magnitudes of STFT (short-time Fourier transform) measurements. The uniqueness of STFT phase retrieval had been established when the signal is one-dimensional function. In this article, we investigate the uniqueness of STFT phase retrieval when the signal is a two-dimensional vector function. And we prove the uniqueness theorem of STFT phase retrieval for bandlimited real-valued and complex-valued vector functions, respectively.","PeriodicalId":54707,"journal":{"name":"Numerical Functional Analysis and Optimization","volume":"44 1","pages":"311 - 331"},"PeriodicalIF":1.2,"publicationDate":"2023-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43414778","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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