Existence of fixed points of asymptotically generalized \Phi-hemicontractive mappings in the intermediate sense

Abstract

Let E be a real Banach space, C be a nonempty closed convex subset of E and T : C → C be a continuous generalized Φ-pseudocontractive mapping, Xiang [Chang He Xiang, Fixed point theorem for generalized Φ-pseudocontractive mappings, Nonlinear Analysis 70 (2009) 2277-2279] proved that T has a unique fixed point in C. It is our purpose in this study to extend the results of Xiang [11] to the class of asymptotically generalized Φ-hemicontractive mappings in the intermediate sense, recently introduced by Okeke, Olaleru and Akewe [6].