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JP Journal of Fixed Point Theory and Applications

Abstract:
Let K be a nonempty closed convex subset of a real reflexive Banach space X that has weakly sequentially continuous duality mapping. In this paper, we consider the viscosity approximation sequence

where

is a weakly contractive mapping,

is a uniformly asymptotically regular sequence of quasi-nonexpansive mappings such that

and

Suppose that

satisfies condition (A). Then it is proved that

converges strongly to a common fixed point p of a family

Our results extend and improve the existing known results in this area.

Keywords and phrases: quasi-nonexpansive mappings, weakly continuous duality mappings, weakly contractive mapping.

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