On the general principle of multi-step fixed point iterative schemes

Abstract

In this study, we establish a general principle for multi-step fixed point iterative schemes in the sense of Rhoades and Soltuz [B.E. Rhoades, S.M. Soltuz, The equivalence between Mann-Ishikawa iterations and multi-step iteration, Nonlinear Analysis 58 (2004), 219-228] to approximate fixed points of the maps satisfying the generic type contractive definition in Banach spaces.