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Abstract
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Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 609281, 9 pages
doi:10.1155/2009/609281

Fixed point theorems in cone Banach spaces

Erdal Karapınar

Abstract

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.