Fixed Point Theorems for Generalized [a, b, c]_p-nonexpansive Mappings in Banach Spaces

The purpose of this paper is to introduce a new class of generalized nonexpansive mappings and establish a fixed point existence result in a uniformly convex Banach space. The convergence analysis of Mann iteration and S-iteration process for this class of mappings has been studied in Banach spaces. By some examples, it is shown that S-iteration process is faster than that of Mann and Ishikawa iteration processes. Our result extends and improves various existing results in literature in the context of S-iteration process.