Generalized mixed equilibrium problems and fixed point problem for a countable family of total quasi-φ-asymptotically nonexpansive mappings in Banach spaces

The purpose of this paper is first to introduce the concept of total quasi-φ-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 for finding 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-φ-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. copyright © 2012 jinhua zhu et al.