Approximate fixed point of uniform hemicontractive mapping and to apply to iterative solution of equation with uniform-accretive mapping

Abstract

The objective of this paper is to introduce the uniform-hemicontractive mapping and to study iterative approximative method for the fixed point of the mappings by Mann iterative sequence with random errors. Let X be a real Banach space and T : X → X an uniformhemicontractive the results presented in this paper show that Mann iterative sequence with random errors converges strongly to an unique fixed point if T is uniformly continuous. Furthermore, if X is uniformly smooth then any continuity of T is unnecessary for the convergence of Mann iterative sequence. As applications, using these results, the iterative solution of nonlinear equation with uniform-accretive mapping is obtained. Mathematics Subject Classification: 47H17, 47H06, 47H10