Convergence theorems for a common fixed point of a finite family of nonself nonexpansive mappings
CE Chidume, Habtu Zegeye, Naseer Shahzad · Fixed Point Theory and Applications · 2005
Abstract Let "Equation missing" be a nonempty closed convex subset of a reflexive real Banach space "Equation missing" which has a uniformly Gâteaux differentiable norm. Assume that "Equation missing" is a sunny nonexpansive retract of "Equation missing" with "Equation missing" as the sunny nonexpansive retraction. Let "Equation missing", "Equation missing", be a family of nonexpansive mappings which are weakly inward. Assume that every nonempty closed bounded convex subset of "Equation missing" has the fixed point property for nonexpansive mappings. A strong convergence theorem is proved for a common fixed point of a family of nonexpansive mappings provided that "Equation missing", "Equation missing", satisfy some mild conditions.