Approximating Fixed Points of Generalized α-Nonexpansive Mappings in Banach Spaces

We introduce a new type of nonexpansive mappings and obtain a number of existence and convergence theorems. This new class of nonlinear mapping properly contains nonexpansive, Suzuki-type generalized nonexpansive mappings and partially extends firmly nonexpansive and α-nonexpansive mappings. Also, this class of mapping need not be continuous. Some useful examples are presented to illustrate facts. Some prominent iteration processes are also compared using numerical computations.