ITERATIVE PROCESS FOR CERTAIN NONLINEAR MAPPINGS IN UNIFORMLY SMOOTH BANACH SPACES

Abstract

A new class of generalized uniformly Lipschitzian mappings is introduced, which includes the known class of uniformly Lipschitzian mappings in Banach spaces as special case. The convergence of the iterative approximation of fixed points for generalized uniformly Lipschitzian asymptotically pseudocontractive mappings by the modified Ishikawa iterative sequences with errors in real Banach sapces is proved. The results presented in this paper extend and improve some recent results by Goebel and Kirk, Schu, Liu, Zhang and others.