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

Fixed Point Theorems in Cone Banach Spaces

Erdal Karapınar

Department of Mathematics, Atılım University, 06836 Ankara, Turkey

Received 23 October 2009; Accepted 15 December 2009

Academic Editor: Juan Jose Nieto

Copyright © 2009 Erdal Karapınar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.