Strong convergence theorem for solving generalized mixed equilibrium problems and fixed point problems for total quasi-φ-asymptotically nonexpansive mappings in Banach spaces

We introduce an iterative scheme for finding a common element of the set of solutions of generalized mixed equilibrium problems and the set of fixed points for countable families of total quasi-φ-asymptotically nonexpansive mappings in banach spaces. we prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm in an uniformly smooth and strictly convex banach space which also enjoys the kadec-klee property. the results presented in this paper improve and extend some recent corresponding results. copyright © 2012 zhaoli ma et al.