Iterative Approximation of Fixed Points of Almost Contractions

In this paper we present a very general class of weakly Picard mappings. The fixed point theorems thus obtained are generalizations of the well-known contraction mapping principle for single-valued mappings and of several of its subsequent generalizations, as well as of the well-known Nadler's fixed point theorem for multi-valued mappings and of many of its recent and very recent extensions. The fixed points are approximated by means of Picard iteration in both single and multi-valued case.