The purpose of this paper is first to introduce the concept of total quasi--asymptotically nonexpansive mapping which contains many kinds of mappings as its special cases and then to use a hybrid algorithm to introduce a new iterative scheme forfinding a common element of the set of solutions for a system of generalized mixed equilibrium problems and the set of common fixed points for a countable family of total quasi--asymptotically nonexpansive mappings. Under suitable conditions some strong convergence theorems are established in an uniformly smooth and strictly convex Banach space with Kadec-Klee property. The results presented in the paper improve and extend some recent results.
"Generalized Mixed Equilibrium Problems and Fixed Point Problem for a Countable Family of Total Quasi--Asymptotically Nonexpansive Mappings in Banach Spaces." J. Appl. Math. 2012 (SI03) 1 - 22, 2012. https://doi.org/10.1155/2012/961560