Generalized Viscosity Implicit Iterative Process for Asymptotically Non-Expansive Mappings in Banach Spaces

Generalized Viscosity Implicit Iterative Process for Asymptotically Non-Expansive Mappings in Banach Spaces

In this paper, we propose a generalized viscosity implicit iterative method for asymptotically non-expansive mappings in Banach spaces. The strong convergence theorem of this algorithm is proved, which solves the variational inequality problem. Moreover, we provide some applications to zero-point pr...

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Main Authors: Chanjuan Pan, Yuanheng Wang
Format: Article
Language:English
Published: MDPI AG 2019-04-01
Series:Mathematics
Subjects:
fixed point
variational inequality
generalized viscosity implicit rule
asymptotically nonexpansive mapping
Banach spaces
Online Access:https://www.mdpi.com/2227-7390/7/5/379
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spelling doaj-20240dca13834e14b101912f2e002c802020-11-25T00:52:42ZengMDPI AGMathematics2227-73902019-04-017537910.3390/math7050379math7050379Generalized Viscosity Implicit Iterative Process for Asymptotically Non-Expansive Mappings in Banach SpacesChanjuan Pan0Yuanheng Wang1Department of Mathematics, Zhejiang Normal University, Jinhua 321004, ChinaDepartment of Mathematics, Zhejiang Normal University, Jinhua 321004, ChinaIn this paper, we propose a generalized viscosity implicit iterative method for asymptotically non-expansive mappings in Banach spaces. The strong convergence theorem of this algorithm is proved, which solves the variational inequality problem. Moreover, we provide some applications to zero-point problems and equilibrium problems. Further, a numerical example is given to illustrate our convergence analysis. The results generalize and improve corresponding results in the literature.https://www.mdpi.com/2227-7390/7/5/379fixed pointvariational inequalitygeneralized viscosity implicit ruleasymptotically nonexpansive mappingBanach spaces
collection DOAJ
language English
format Article
sources DOAJ
author Chanjuan Pan
Yuanheng Wang
spellingShingle Chanjuan Pan
Yuanheng Wang
Generalized Viscosity Implicit Iterative Process for Asymptotically Non-Expansive Mappings in Banach Spaces
Mathematics
fixed point
variational inequality
generalized viscosity implicit rule
asymptotically nonexpansive mapping
Banach spaces
author_facet Chanjuan Pan
Yuanheng Wang
author_sort Chanjuan Pan
title Generalized Viscosity Implicit Iterative Process for Asymptotically Non-Expansive Mappings in Banach Spaces
title_short Generalized Viscosity Implicit Iterative Process for Asymptotically Non-Expansive Mappings in Banach Spaces
title_full Generalized Viscosity Implicit Iterative Process for Asymptotically Non-Expansive Mappings in Banach Spaces
title_fullStr Generalized Viscosity Implicit Iterative Process for Asymptotically Non-Expansive Mappings in Banach Spaces
title_full_unstemmed Generalized Viscosity Implicit Iterative Process for Asymptotically Non-Expansive Mappings in Banach Spaces
title_sort generalized viscosity implicit iterative process for asymptotically non-expansive mappings in banach spaces
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2019-04-01
description In this paper, we propose a generalized viscosity implicit iterative method for asymptotically non-expansive mappings in Banach spaces. The strong convergence theorem of this algorithm is proved, which solves the variational inequality problem. Moreover, we provide some applications to zero-point problems and equilibrium problems. Further, a numerical example is given to illustrate our convergence analysis. The results generalize and improve corresponding results in the literature.
topic fixed point
variational inequality
generalized viscosity implicit rule
asymptotically nonexpansive mapping
Banach spaces
url https://www.mdpi.com/2227-7390/7/5/379
work_keys_str_mv AT chanjuanpan generalizedviscosityimplicititerativeprocessforasymptoticallynonexpansivemappingsinbanachspaces
AT yuanhengwang generalizedviscosityimplicititerativeprocessforasymptoticallynonexpansivemappingsinbanachspaces
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