Strong Convergence Theorems for Countable Families of Uniformly Quasi‐ϕ‐Asymptotically Nonexpansive Mappings and a System of Generalized Mixed Equilibrium Problems
Siwaporn Saewan, Poom Kumam · Abstract and Applied Analysis · 2011
The purpose of this paper is to present a new hybrid block iterative scheme by the generalized f‐ projection method for finding a common element of the fixed point set for a countable family of uniformly quasi‐ϕ‐asymptotically nonexpansive mappings and the set of solutions of the system of generalized mixed equilibrium problems in a strictly convex and uniformly smooth Banach space with the Kadec‐Klee property. Furthermore, we prove that our new iterative scheme converges strongly to a common element of the aforementioned sets. The results presented in this paper improve and extend important recent results in the literature.