Approximating fixed points of α-convex generalized nonexpansive mappings

Abstract

The objective of our paper is to introduce a novel category of nonlinear mappings namely α-convex generalized nonexpansive and demonstrate different existence and convergence theorems for this type of mappings in Banach spaces under various assumptions. We show that this class of mappings admits an approximate fixed point sequence in each nonempty bounded closed convex Φ-invariant subset of Banach spaces. Moreover, we provide an example to support the results presented in our study. Furthermore, we expand upon the findings reported by T. Suzuki (J. Math. Anal. Appl., 340(2): 1088–1095, 2008).