A fixed point theorem for monotone asyptotic nonexpansive mappings

2016/06/21 by Monther Rashed Alfuraidan, Alfuraidan, Monther Rashed, Mohamed A. Khamsi +1
Mathematics · Computer Science · #Fixed Point Theorems Analysis #Optimization and Variational Analysis #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.1606.06469

Abstract

Let C be a nonempty, bounded, closed, and convex subset of a Banach space X and T : C → C be a monotone asymptotic nonexpansive mapping. In this paper, we investigate the existence of fixed points of T. In particular, we establish an analogue to the original Goebel and Kirk's fixed point theorem for asymptotic nonexpansive mappings.

Related

• Fixed points for mappings of asymptotically nonexpansive type
• Fixed point theorems for asymptotically contractive mappings
• Approximating fixed points of asymptotically nonexpansive mappings in\n Banach spaces by metric projections
• Fixed points of asymptotically nonexpansive mappings with center 0 and applications
• Construction of fixed points of asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces