Opial’s Condition and Fixed Point for Nonexpansive Mapping in Banach spaces

Opial’s condition plays an important role in the study of weak convergence of iterates and random products of nonexpansive mappings and of the asymptotic behavior of nonlinear semigroups. In this paper, we prove the weak convergence of a modified Noor iteration for nonself I- nonexpansive mapping in a Banach space which satisfies Opial’s condition. Finally a fixed point theorem for multivalued nonexpansive mappings in a Banach space satisfying this condition is proved

Keywords:

Opial’s Condition , Nonexpansive Mappings , Fixed Point , Banach spaces