Fixed Point Theorems in Cone Banach Spaces

Fixed Point Theorems in Cone Banach Spaces

In this manuscript, a class of self-mappings on cone Banach spaces which have at least one fixed point is considered. More precisely, for a closed and convex subset C of a cone Banach space with the norm ∥x∥P=d(x,0), if there exist a, b, s and T:C→C satisfies the...

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Main Author: Erdal Karapınar
Format: Article
Language:English
Published: SpringerOpen 2009-01-01
Series:Fixed Point Theory and Applications
Online Access:http://dx.doi.org/10.1155/2009/609281
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spelling doaj-687a14209b35489bbbc060fa19071b212020-11-24T22:02:43ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122009-01-01200910.1155/2009/609281Fixed Point Theorems in Cone Banach SpacesErdal KarapınarIn this manuscript, a class of self-mappings on cone Banach spaces which have at least one fixed point is considered. More precisely, for a closed and convex subset C of a cone Banach space with the norm ∥x∥P=d(x,0), if there exist a, b, s and T:C→C satisfies the conditions 0≤s+|a|−2b<2(a+b) and 4ad(Tx,Ty)+b(d(x,Tx)+d(y,Ty))≤sd(x,y) for all x,y∈C , then T has at least one Fixed point. http://dx.doi.org/10.1155/2009/609281
collection DOAJ
language English
format Article
sources DOAJ
author Erdal Karapınar
spellingShingle Erdal Karapınar
Fixed Point Theorems in Cone Banach Spaces
Fixed Point Theory and Applications
author_facet Erdal Karapınar
author_sort Erdal Karapınar
title Fixed Point Theorems in Cone Banach Spaces
title_short Fixed Point Theorems in Cone Banach Spaces
title_full Fixed Point Theorems in Cone Banach Spaces
title_fullStr Fixed Point Theorems in Cone Banach Spaces
title_full_unstemmed Fixed Point Theorems in Cone Banach Spaces
title_sort fixed point theorems in cone banach spaces
publisher SpringerOpen
series Fixed Point Theory and Applications
issn 1687-1820
1687-1812
publishDate 2009-01-01
description In this manuscript, a class of self-mappings on cone Banach spaces which have at least one fixed point is considered. More precisely, for a closed and convex subset C of a cone Banach space with the norm ∥x∥P=d(x,0), if there exist a, b, s and T:C→C satisfies the conditions 0≤s+|a|−2b<2(a+b) and 4ad(Tx,Ty)+b(d(x,Tx)+d(y,Ty))≤sd(x,y) for all x,y∈C , then T has at least one Fixed point.
url http://dx.doi.org/10.1155/2009/609281
work_keys_str_mv AT erdalkarapampx131nar fixedpointtheoremsinconebanachspaces
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