A new monotone hybrid algorithm for a convex feasibiliy problem for an infinite family of nonexpansive-type maps, with applications

Abstract

Let C be a nonempty closed and convex subset of a uniformly smooth and uniformly convex real Banach space E with dual space E ∗ . A new monotone hybrid method for finding a common element for a family of a general class of nonlinear nonexpansive maps is constructed and, the sequence of the method is proved to converge strongly to a common element of the family. Finally, application of this theorem complements, generalizes and extends some recent important results.