Convergence theorems from monotone hybrid methods for an infinitely countable family of Lipschitz asymptotically quasi-nonexpansive mappings

In this paper, we prove a weak convergence theorem for the modified Mann iteration process for a uniformly Lipschitzian and asymptotically quasi-nonexpansive mapping in a uniformly convex Banach space. We also introduce two new kinds of monotone hybrid methods and obtain strong convergence theorems...

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Main Authors:	Watcharaporn Cholamjiak, Suthep Suantai
Format:	Journal
Published:	2018
Subjects:	Computer Science Engineering Mathematics
Online Access:	https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=77955589557&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/50713
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Institution:	Chiang Mai University

id	th-cmuir.6653943832-50713
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spelling	th-cmuir.6653943832-507132018-09-04T04:49:26Z Convergence theorems from monotone hybrid methods for an infinitely countable family of Lipschitz asymptotically quasi-nonexpansive mappings Watcharaporn Cholamjiak Suthep Suantai Computer Science Engineering Mathematics In this paper, we prove a weak convergence theorem for the modified Mann iteration process for a uniformly Lipschitzian and asymptotically quasi-nonexpansive mapping in a uniformly convex Banach space. We also introduce two new kinds of monotone hybrid methods and obtain strong convergence theorems for an infinitely countable family of uniformly Lipschitzian and asymptotically quasi-nonexpansive mappings in a Hilbert space. The results of this paper improve on and extend corresponding ones announced by many authors. © 2009. 2018-09-04T04:44:38Z 2018-09-04T04:44:38Z 2010-08-01 Journal 1751570X 2-s2.0-77955589557 10.1016/j.nahs.2009.12.003 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=77955589557&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/50713
institution	Chiang Mai University
building	Chiang Mai University Library
country	Thailand
collection	CMU Intellectual Repository
topic	Computer Science Engineering Mathematics
spellingShingle	Computer Science Engineering Mathematics Watcharaporn Cholamjiak Suthep Suantai Convergence theorems from monotone hybrid methods for an infinitely countable family of Lipschitz asymptotically quasi-nonexpansive mappings
description	In this paper, we prove a weak convergence theorem for the modified Mann iteration process for a uniformly Lipschitzian and asymptotically quasi-nonexpansive mapping in a uniformly convex Banach space. We also introduce two new kinds of monotone hybrid methods and obtain strong convergence theorems for an infinitely countable family of uniformly Lipschitzian and asymptotically quasi-nonexpansive mappings in a Hilbert space. The results of this paper improve on and extend corresponding ones announced by many authors. © 2009.
format	Journal
author	Watcharaporn Cholamjiak Suthep Suantai
author_facet	Watcharaporn Cholamjiak Suthep Suantai
author_sort	Watcharaporn Cholamjiak
title	Convergence theorems from monotone hybrid methods for an infinitely countable family of Lipschitz asymptotically quasi-nonexpansive mappings
title_short	Convergence theorems from monotone hybrid methods for an infinitely countable family of Lipschitz asymptotically quasi-nonexpansive mappings
title_full	Convergence theorems from monotone hybrid methods for an infinitely countable family of Lipschitz asymptotically quasi-nonexpansive mappings
title_fullStr	Convergence theorems from monotone hybrid methods for an infinitely countable family of Lipschitz asymptotically quasi-nonexpansive mappings
title_full_unstemmed	Convergence theorems from monotone hybrid methods for an infinitely countable family of Lipschitz asymptotically quasi-nonexpansive mappings
title_sort	convergence theorems from monotone hybrid methods for an infinitely countable family of lipschitz asymptotically quasi-nonexpansive mappings
publishDate	2018
url	https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=77955589557&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/50713
_version_	1681423639468048384

Convergence theorems from monotone hybrid methods for an infinitely countable family of Lipschitz asymptotically quasi-nonexpansive mappings

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