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 -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.
Yekini Shehu. "Strong Convergence Theorems for Families of Weak Relatively Nonexpansive Mappings." Abstr. Appl. Anal. 2011 1 - 19, 2011. https://doi.org/10.1155/2011/251612