A new modified Krasnoselskii-Mann-type algorithm for an infinite family of multivalued quasi-nonexpansive mappings in unformly convexe spaces

Abstract

The main objective of this paper is to introduce and study a new modified Krasnoselskii-Mann-type method for approximating a common fixed points of an infinite family of multivalued quasi-nonexpansive mappings in real Banach spaces. Under suitable assumptions, we prove the strong convergence of this algorithm in uniformly convex real Banach spaces without imposing any compactness assumption. Application to minimum-norm fixed point problem is provided to support our main results. Futhermore, numerical example is given to demonstrate the implementability of our algorithm. Finally, our algorithm generalize and extend of the existing results in the literature and moreover, its computationaly effort is less per each iteration compared with related works.