Viscosity Approximation Methods in Reflexive Banach Spaces with a Sequence of Contractions

Abstract

The aim of this paper is to study viscosity approximation methods in re exive Banach spaces. Let E be a re exive Banach space which admits a weakly sequentially continuous duality mapping  a nonempty closed convex subset of   a sequence of contractions on C and Tn, n = 1, 2, 3, · · ·N a nite family of nonexpansive mappings on C.  We show that under appropriate conditions on κ the implicit iterative sequence τ dened by                                           where κ ∈ (0, 1)  converges strongly to a common xed point  . We further show that the results hold for an innite family   of nonexpansive mappings.