Strong convergence theorem for solving generalized mixed equilibrium problems and fixed point problems for total quasi-\(\phi\)-asymptotically nonexpansive mappings in Banach spaces (Q442943)

Summary: 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-\(\phi\)-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.