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

G. V. R. Babu and G. N. Alemay

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.