Strong Convergence Theorems for Families of Weak Relatively Nonexpansive Mappings

Abstract

We construct a new Halpern type iterative scheme by hybrid methods and prove strong convergence theorem for approximation of a common fixed point of two countable families of weak relatively nonexpansive mappings in a uniformly convex and uniformly smooth real Banach space using the properties of generalized $f$-projection operator. Using this result, we discuss strong convergence theorem concerning general $H$-monotone mappings. Our results extend many known recent results in the literature.