A New Hybrid Algorithm for a Pair of Quasi‐ϕ‐Asymptotically Nonexpansive Mappings and Generalized Mixed Equilibrium Problems in Banach Spaces
Jinhua Zhu, Shih-sen Chang · International Journal of Mathematics and Mathematical Sciences · 2011
The purpose of this paper is, by using a new hybrid method, to prove a strong convergence theorem for finding a common element of the set of solutions for a generalized mixed equilibrium problem, the set of solutions for a variational inequality problem, and the set of common fixed points for a pair of quasi‐ϕ‐asymptotically nonexpansive mappings. Under suitable conditions some strong convergence theorems are established in a uniformly smooth and strictly convex Banach space with Kadec‐Klee property. The results presented in the paper improve and extend some recent results.