{"title":"A viscosity method with inertial effects for split common fixed point problems of demicontractive mappings","authors":"","doi":"10.23952/jnfa.2022.17","DOIUrl":null,"url":null,"abstract":". In this paper, we first propose a new algorithm for the split common fixed point problems of demicontractive mappings based on viscosity methods and inertial effects in Hilbert spaces. The algorithm is constructed in such a way that its step sizes are not related to the norm of a bounded linear operator. Then, we prove some strong convergence theorems under some suitable conditions. Finally, we provide a numerical example to show the effectiveness of our proposed algorithm. Our results generalize and improve some known results announced recently.","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":"1 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Nonlinear Functional Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.23952/jnfa.2022.17","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 3
Abstract
. In this paper, we first propose a new algorithm for the split common fixed point problems of demicontractive mappings based on viscosity methods and inertial effects in Hilbert spaces. The algorithm is constructed in such a way that its step sizes are not related to the norm of a bounded linear operator. Then, we prove some strong convergence theorems under some suitable conditions. Finally, we provide a numerical example to show the effectiveness of our proposed algorithm. Our results generalize and improve some known results announced recently.
期刊介绍：
Journal of Nonlinear Functional Analysis focuses on important developments in nonlinear functional analysis and its applications with a particular emphasis on topics include, but are not limited to: Approximation theory; Asymptotic behavior; Banach space geometric constant and its applications; Complementarity problems; Control theory; Dynamic systems; Fixed point theory and methods of computing fixed points; Fluid dynamics; Functional differential equations; Iteration theory, iterative and composite equations; Mathematical biology and ecology; Miscellaneous applications of nonlinear analysis; Multilinear algebra and tensor computation; Nonlinear eigenvalue problems and nonlinear spectral theory; Nonsmooth analysis, variational analysis, convex analysis and their applications; Numerical analysis; Optimal control; Optimization theory; Ordinary differential equations; Partial differential equations; Positive operator inequality and its applications in operator equation spectrum theory and so forth; Semidefinite programming polynomial optimization; Variational and other types of inequalities involving nonlinear mappings; Variational inequalities.
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