International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 17, Pages 2711-2718
doi:10.1155/IJMMS.2005.2711

Iterative approximation of fixed point for Φ-hemicontractive mapping without Lipschitz assumption

Abstract

Let E be an arbitrary real Banach space and let K be a nonempty closed convex subset of E such that K+K⊂K. Assume that T:K→K is a uniformly continuous and Φ-hemicontractive mapping. It is shown that the Ishikawa iterative sequence with errors converges strongly to the unique fixed point of T.