Convergence of an Ishikawa iteration scheme for nonlinear quasi-contractive mappings in convex metric spaces

Abstract

In this paper, we show that the Ishikawa iteration scheme for a nonlinear quasicontractive selfmap of a nonempty closed convex subset of a complete convex metric space, converges to the unique fixed point. Our theorem generalizes Ciric's result (1999) and partially solves an open problem of Ciric [5].