Some iterative algorithms for approximating solutions of nonlinear operator equations in Banach spaces

Abstract

In this paper, iterative algorithms of Krasnoselkii-type and of Halpern-type for approximating an element of the set of common zeros of a countable family of inverse strongly monotone maps, common fixed points of a countable family of totally quasi- $$\phi $$ -asymptotically nonexpansive nonself multi-valued maps, and a solution of a system of generalized mixed equilibrium problems are constructed and studied. Strong convergence of the sequences generated by these algorithms is established in uniformly smooth and 2-uniformly convex real Banach spaces. The theorems obtained extend, improve and generalize several recent important results.