A Krasnoselskii-type algorithm for approximating zeros of monotone maps in Banach spaces with applications

Abstract

In this paper, a Krasnoselskii-type algorithm that approximates the unique zero of a Hölder continuous and strongly monotone map is constructed. Strong convergence of the sequence generated by this algorithm is established in strictly convex, reflexive and smooth real Banach spaces. Results obtained in this paper are applied to approximate a minimizer of some convex functionals and a solution of a Hammerstein integral equation.