Fixed point solutions of variational inequalities for a semigroup of asymptotically nonexpansive mappings in Banach spaces
Pongsakorn Sunthrayuth, Poom Kumam · Fixed Point Theory and Applications · 2012
The purpose of this article is to introduce two iterative algorithms for finding a common fixed point of a semigroup of asymptotically nonexpansive mappings which is a unique solution of some variational inequality. We provide two algorithms, one implicit and another explicit, from which strong convergence theorems are obtained in a uniformly convex Banach space, which admits a weakly continuous duality mapping. The results in this article improve and extend the recent ones announced by Li et al. (Nonlinear Anal. 70:3065-3071, 2009), Zegeye et al. (Math. Comput. Model. 54:2077-2086, 2011) and many others. MSC: 47H05, 47H09, 47H20, 47J25.