Approximating common fixed points for a finite family of non-lipschitzian mappings in banach spaces

Abstract

In this paper, we introduce multi-step iterative scheme with errors for a finite family of asymptotically nonexpansive mappings in the intermediate sense. Mann-type, Ishikawa-type and Noor-type iterations are covered by the new iterative scheme. Weak and strong convergence theorems for the iterative scheme in a uniformly convex Banach space are established under some conditions which are weaker than demicompactness or completely continuous. Our results improve and generalize the recent known results in the literature.