New algorithms for solving system of generalized mixed equilibrium problems and some nonlinear problems, with applications

In this paper, new iterative algorithms of Krasnoselkii-type and Halpern-type for approximating common fixed points of a countable family of equally continuous and totally quasi-phi-asymptotically nonexpansive maps, common zeros of a countable family of -inverse strongly monotone maps and a common element of a set of solutions to a system of generalized mixed equilibrium problems in a 2-uniformly convex and uniformly smooth real Banach space are introduced and studied. Our theorems are significant improvements of some recent important results, in particular, the results of Deng (J Fixed Point Theory appl. 2016); Ofoedu and Malonza (Appl Math Comput. 2011;217:6019-6030), and Wang et al. (Fixed Point Theory Appl. 2012;34).