Strong Convergence of Mann Iteration for a Hybrid Pair of Mappings in a Banach Space

Abstract

We prove the strong convergence of Mann iteration for a hybrid pair of maps to a common fixed point of a selfmap f and a multi-valued f-nonexpansive mapping T in Banach space E. Our result extend Theorem 2.3 of Song and Wang [Y. Song, H. Wang, Convergence of iterative algorithms for multi-valued mappings in Banach spaces, Nonlinear Analysis, 70 (2009), 1547–1556] to a hybrid pair of maps. Mathematics Subject Classification: 54 H 25 Keywords: Strong convergence, Mann iteration, common fixed point, Multi-valued nonexpansive mapping