Abstract
The aim of this paper is to introduce multistep generalized viscosity iterative algorithm for a finite family of nonexpansive mappings in the framework of reflexive Banach spaces with a weakly sequentially continuous duality mapping and uniformly smooth Banach spaces. Our proposed iterative algorithm converges in norm to a common fixed point of a finite family of nonexpansive mappings which in addition solves a variational inequality. Projection methods for solving the convex feasibility problem are studied. Our results improve the recent results of Duan and He (2014), Yao et al. (2008), Kim and Xu (2005), Xu (2004), Moudafi (2000) and Wittmann (1992).