A modified viscosity implicit-type proximal point algorithm for monotone inclusions and asymptotically nonexpansive mappings in Hadamard spaces

A modified viscosity implicit-type proximal point algorithm for monotone inclusions and asymptotically nonexpansive mappings in Hadamard spaces

Abstract The purpose of this article is to propose a modified viscosity implicit-type proximal point algorithm for approximating a common solution of a monotone inclusion problem and a fixed point problem for an asymptotically nonexpansive mapping in Hadamard spaces. Under suitable conditions, some...

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Main Authors: Shih-sen Chang, Jen-Chih Yao, Ching-Feng Wen, Lin Wang
Format: Article
Language:English
Published: SpringerOpen 2018-09-01
Series:Journal of Inequalities and Applications
Subjects:
Hadamard space
CAT(0) space
Viscosity implicit approximation methods
Monotone mapping
Proximal point algorithm
Online Access:http://link.springer.com/article/10.1186/s13660-018-1825-5
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spelling doaj-e718576a3785415384675197ec2bc3c02020-11-25T01:38:21ZengSpringerOpenJournal of Inequalities and Applications1029-242X2018-09-012018111410.1186/s13660-018-1825-5A modified viscosity implicit-type proximal point algorithm for monotone inclusions and asymptotically nonexpansive mappings in Hadamard spacesShih-sen Chang0Jen-Chih Yao1Ching-Feng Wen2Lin Wang3Center for General Education, China Medical UniversityCenter for General Education, China Medical UniversityCenter for Fundamental Science; and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical UniversityCollege of Statistics and Mathematics, Yunnan University of Finance and EconomicsAbstract The purpose of this article is to propose a modified viscosity implicit-type proximal point algorithm for approximating a common solution of a monotone inclusion problem and a fixed point problem for an asymptotically nonexpansive mapping in Hadamard spaces. Under suitable conditions, some strong convergence theorems of the proposed algorithms to such a common solution are proved. Our results extend and complement some recent results in this direction.http://link.springer.com/article/10.1186/s13660-018-1825-5Hadamard spaceCAT(0) spaceViscosity implicit approximation methodsMonotone mappingProximal point algorithm
collection DOAJ
language English
format Article
sources DOAJ
author Shih-sen Chang
Jen-Chih Yao
Ching-Feng Wen
Lin Wang
spellingShingle Shih-sen Chang
Jen-Chih Yao
Ching-Feng Wen
Lin Wang
A modified viscosity implicit-type proximal point algorithm for monotone inclusions and asymptotically nonexpansive mappings in Hadamard spaces
Journal of Inequalities and Applications
Hadamard space
CAT(0) space
Viscosity implicit approximation methods
Monotone mapping
Proximal point algorithm
author_facet Shih-sen Chang
Jen-Chih Yao
Ching-Feng Wen
Lin Wang
author_sort Shih-sen Chang
title A modified viscosity implicit-type proximal point algorithm for monotone inclusions and asymptotically nonexpansive mappings in Hadamard spaces
title_short A modified viscosity implicit-type proximal point algorithm for monotone inclusions and asymptotically nonexpansive mappings in Hadamard spaces
title_full A modified viscosity implicit-type proximal point algorithm for monotone inclusions and asymptotically nonexpansive mappings in Hadamard spaces
title_fullStr A modified viscosity implicit-type proximal point algorithm for monotone inclusions and asymptotically nonexpansive mappings in Hadamard spaces
title_full_unstemmed A modified viscosity implicit-type proximal point algorithm for monotone inclusions and asymptotically nonexpansive mappings in Hadamard spaces
title_sort modified viscosity implicit-type proximal point algorithm for monotone inclusions and asymptotically nonexpansive mappings in hadamard spaces
publisher SpringerOpen
series Journal of Inequalities and Applications
issn 1029-242X
publishDate 2018-09-01
description Abstract The purpose of this article is to propose a modified viscosity implicit-type proximal point algorithm for approximating a common solution of a monotone inclusion problem and a fixed point problem for an asymptotically nonexpansive mapping in Hadamard spaces. Under suitable conditions, some strong convergence theorems of the proposed algorithms to such a common solution are proved. Our results extend and complement some recent results in this direction.
topic Hadamard space
CAT(0) space
Viscosity implicit approximation methods
Monotone mapping
Proximal point algorithm
url http://link.springer.com/article/10.1186/s13660-018-1825-5
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AT jenchihyao amodifiedviscosityimplicittypeproximalpointalgorithmformonotoneinclusionsandasymptoticallynonexpansivemappingsinhadamardspaces
AT chingfengwen amodifiedviscosityimplicittypeproximalpointalgorithmformonotoneinclusionsandasymptoticallynonexpansivemappingsinhadamardspaces
AT linwang amodifiedviscosityimplicittypeproximalpointalgorithmformonotoneinclusionsandasymptoticallynonexpansivemappingsinhadamardspaces
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