Hybrid Methods for a Countable Family of G-Nonexpansive Mappings in Hilbert Spaces Endowed with Graphs

Hybrid Methods for a Countable Family of G-Nonexpansive Mappings in Hilbert Spaces Endowed with Graphs

In this paper, we introduce the iterative scheme for finding a common fixed point of a countable family of G-nonexpansive mappings by the shrinking projection method which generalizes Takahashi Takeuchi and Kubota’s theorem in a Hilbert space with a directed graph. Simultaneously, we give...

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Main Authors: Suthep Suantai, Mana Donganont, Watcharaporn Cholamjiak
Format: Article
Language:English
Published: MDPI AG 2019-10-01
Series:Mathematics
Subjects:
g-nonexpansive mapping
hybrid method
<i>nst</i>-condition
iteration
hilbert space
Online Access:https://www.mdpi.com/2227-7390/7/10/936
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spelling doaj-fc319d0db85a4ffea9f9f0ee923caca42020-11-25T00:39:17ZengMDPI AGMathematics2227-73902019-10-0171093610.3390/math7100936math7100936Hybrid Methods for a Countable Family of G-Nonexpansive Mappings in Hilbert Spaces Endowed with GraphsSuthep Suantai0Mana Donganont1Watcharaporn Cholamjiak2Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, ThailandSchool of Science, University of Phayao, Phayao 56000, ThailandSchool of Science, University of Phayao, Phayao 56000, ThailandIn this paper, we introduce the iterative scheme for finding a common fixed point of a countable family of G-nonexpansive mappings by the shrinking projection method which generalizes Takahashi Takeuchi and Kubota&#8217;s theorem in a Hilbert space with a directed graph. Simultaneously, we give examples and numerical results for supporting our main theorems and compare the rate of convergence of some examples under the same conditions.https://www.mdpi.com/2227-7390/7/10/936g-nonexpansive mappinghybrid method<i>nst</i>-conditioniterationhilbert space
collection DOAJ
language English
format Article
sources DOAJ
author Suthep Suantai
Mana Donganont
Watcharaporn Cholamjiak
spellingShingle Suthep Suantai
Mana Donganont
Watcharaporn Cholamjiak
Hybrid Methods for a Countable Family of G-Nonexpansive Mappings in Hilbert Spaces Endowed with Graphs
Mathematics
g-nonexpansive mapping
hybrid method
<i>nst</i>-condition
iteration
hilbert space
author_facet Suthep Suantai
Mana Donganont
Watcharaporn Cholamjiak
author_sort Suthep Suantai
title Hybrid Methods for a Countable Family of G-Nonexpansive Mappings in Hilbert Spaces Endowed with Graphs
title_short Hybrid Methods for a Countable Family of G-Nonexpansive Mappings in Hilbert Spaces Endowed with Graphs
title_full Hybrid Methods for a Countable Family of G-Nonexpansive Mappings in Hilbert Spaces Endowed with Graphs
title_fullStr Hybrid Methods for a Countable Family of G-Nonexpansive Mappings in Hilbert Spaces Endowed with Graphs
title_full_unstemmed Hybrid Methods for a Countable Family of G-Nonexpansive Mappings in Hilbert Spaces Endowed with Graphs
title_sort hybrid methods for a countable family of g-nonexpansive mappings in hilbert spaces endowed with graphs
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2019-10-01
description In this paper, we introduce the iterative scheme for finding a common fixed point of a countable family of G-nonexpansive mappings by the shrinking projection method which generalizes Takahashi Takeuchi and Kubota&#8217;s theorem in a Hilbert space with a directed graph. Simultaneously, we give examples and numerical results for supporting our main theorems and compare the rate of convergence of some examples under the same conditions.
topic g-nonexpansive mapping
hybrid method
<i>nst</i>-condition
iteration
hilbert space
url https://www.mdpi.com/2227-7390/7/10/936
work_keys_str_mv AT suthepsuantai hybridmethodsforacountablefamilyofgnonexpansivemappingsinhilbertspacesendowedwithgraphs
AT manadonganont hybridmethodsforacountablefamilyofgnonexpansivemappingsinhilbertspacesendowedwithgraphs
AT watcharaporncholamjiak hybridmethodsforacountablefamilyofgnonexpansivemappingsinhilbertspacesendowedwithgraphs
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