On Generalized Nonexpansive Maps in Banach Spaces

We introduce a very general class of generalized non-expansive maps. This new class of maps properly includes the class of Suzuki non-expansive maps, Reich–Suzuki type non-expansive maps, and generalized <inline-formula> <math display="inline"> <semantics> <mi>α<...

Full description

Bibliographic Details
Main Authors:	Kifayat Ullah, Junaid Ahmad, Manuel de la Sen
Format:	Article
Language:	English
Published:	MDPI AG 2020-07-01
Series:	Computation
Subjects:	generalized non-expansive map demiclosed principle uniformly convex Banach space rate of convergence Banach space
Online Access:	https://www.mdpi.com/2079-3197/8/3/61

id	doaj-0f73eff0bd954a45a015272a031a934b
record_format	Article
spelling	doaj-0f73eff0bd954a45a015272a031a934b2020-11-25T03:06:48ZengMDPI AGComputation2079-31972020-07-018616110.3390/computation8030061On Generalized Nonexpansive Maps in Banach SpacesKifayat Ullah0Junaid Ahmad1Manuel de la Sen2Department of Mathematics, University of Science and Technology, Bannu 28100, Khyber Pakhtunkhwa, PakistanDepartment of Mathematics, University of Science and Technology, Bannu 28100, Khyber Pakhtunkhwa, PakistanInstitute of Research and Development of Processes, University of the Basque Country, Campus of Leioa (Bizkaia), P.O. Box 644- Bilbao, Barrio Sarriena, 48940 Leioa, SpainWe introduce a very general class of generalized non-expansive maps. This new class of maps properly includes the class of Suzuki non-expansive maps, Reich–Suzuki type non-expansive maps, and generalized <inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula>-non-expansive maps. We establish some basic properties and demiclosed principle for this class of maps. After this, we establish existence and convergence results for this class of maps in the context of uniformly convex Banach spaces and compare several well known iterative algorithms.https://www.mdpi.com/2079-3197/8/3/61generalized non-expansive mapdemiclosed principleuniformly convex Banach spacerate of convergenceBanach space
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Kifayat Ullah Junaid Ahmad Manuel de la Sen
spellingShingle	Kifayat Ullah Junaid Ahmad Manuel de la Sen On Generalized Nonexpansive Maps in Banach Spaces Computation generalized non-expansive map demiclosed principle uniformly convex Banach space rate of convergence Banach space
author_facet	Kifayat Ullah Junaid Ahmad Manuel de la Sen
author_sort	Kifayat Ullah
title	On Generalized Nonexpansive Maps in Banach Spaces
title_short	On Generalized Nonexpansive Maps in Banach Spaces
title_full	On Generalized Nonexpansive Maps in Banach Spaces
title_fullStr	On Generalized Nonexpansive Maps in Banach Spaces
title_full_unstemmed	On Generalized Nonexpansive Maps in Banach Spaces
title_sort	on generalized nonexpansive maps in banach spaces
publisher	MDPI AG
series	Computation
issn	2079-3197
publishDate	2020-07-01
description	We introduce a very general class of generalized non-expansive maps. This new class of maps properly includes the class of Suzuki non-expansive maps, Reich–Suzuki type non-expansive maps, and generalized <inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula>-non-expansive maps. We establish some basic properties and demiclosed principle for this class of maps. After this, we establish existence and convergence results for this class of maps in the context of uniformly convex Banach spaces and compare several well known iterative algorithms.
topic	generalized non-expansive map demiclosed principle uniformly convex Banach space rate of convergence Banach space
url	https://www.mdpi.com/2079-3197/8/3/61
work_keys_str_mv	AT kifayatullah ongeneralizednonexpansivemapsinbanachspaces AT junaidahmad ongeneralizednonexpansivemapsinbanachspaces AT manueldelasen ongeneralizednonexpansivemapsinbanachspaces
_version_	1724672259929407488

On Generalized Nonexpansive Maps in Banach Spaces

Similar Items