Fixed point theorems in cone Banach spaces

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. Copyright © 2009 Erdal Karapinar.