{"title":"APPROXIMATION OF ZEROS OF SUM OF MONOTONE MAPPINGS WITH APPLICATIONS TO VARIATIONAL INEQUALITY AND IMAGE RESTORATION PROBLEMS","authors":"A. Adamu, Jitsupa Deepho, A. Ibrahim, A. Abubakar","doi":"10.22771/NFAA.2021.26.02.12","DOIUrl":null,"url":null,"abstract":"In this paper, an inertial Halpern-type forward backward iterative algorithm for approximating solution of a monotone inclusion problem whose solution is also a fixed point of some nonlinear mapping is introduced and studied. Strong convergence theorem is established in a real Hilbert space. Furthermore, our theorem is applied to variational inequality problems, convex minimization problems and image restoration problems. Finally, numerical illustrations are presented to support the main theorem and its applications.","PeriodicalId":37534,"journal":{"name":"Nonlinear Functional Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Functional Analysis and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22771/NFAA.2021.26.02.12","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 9
Abstract
In this paper, an inertial Halpern-type forward backward iterative algorithm for approximating solution of a monotone inclusion problem whose solution is also a fixed point of some nonlinear mapping is introduced and studied. Strong convergence theorem is established in a real Hilbert space. Furthermore, our theorem is applied to variational inequality problems, convex minimization problems and image restoration problems. Finally, numerical illustrations are presented to support the main theorem and its applications.
期刊介绍：
The international mathematical journal NFAA will publish carefully selected original research papers on nonlinear functional analysis and applications, that is, ordinary differential equations, all kinds of partial differential equations, functional differential equations, integrodifferential equations, control theory, approximation theory, optimal control, optimization theory, numerical analysis, variational inequality, asymptotic behavior, fixed point theory, dynamic systems and complementarity problems. Papers for publication will be communicated and recommended by the members of the Editorial Board.
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