Approximating Common Fixed Points of Nonexpansive Mappings in Banach Spaces
Naseer Shahzad, Reem Al-Dubiban Β· Georgian Mathematical Journal Β· 2006
Abstract Let πΎ be a nonempty closed convex subset of a real uniformly convex Banach space πΈ and π, π : πΎ β πΎ two nonexpansive mappings such that πΉ(π) β© πΉ(π) := {π₯ β πΎ : ππ₯ = ππ₯ = π₯} β ΓΈ. Suppose {π₯π} is generated iteratively by π₯1 β πΎ, π₯π+1 = (1 β Ξ± π)π₯π + Ξ± ππ[(1 β Ξ² π)π₯π + Ξ² πππ₯π], π β₯ 1, where {Ξ± π}, {Ξ² π} are real sequences in [0, 1]. In this paper, we discuss the weak and strong convergence of {π₯π} to some π₯* β πΉ(π) β© πΉ(π).