In this paper, we study an iterative process for approx-imating a common fixed point of afamily of uniformly asymptotically regular asymptotically nonexpansive mappings with variational inequality problem in uniformly convex Banach space with uniformly Gâteaux differentiable norm. We prove a strong convergence theorem under some suitable conditions. Our result is applicable in Lp(ℓp) spaces, 1 < p < ∞ (and consequently in Sobolev spaces). Our results improve and general-ize some well-known results in the literature.
- Asymptotically non-expansive mapping
- Fixed point
- Variational inequality
- µ-strictly pseudocontractive mapping
- η-strongly accretive maps