Strong Convergence of Cesàro Mean Iterations for Nonexpansive Nonself-Mappings in Banach Spaces
Rabian Wangkeeree · Fixed Point Theory and Applications · 2007
Abstract Let "Equation missing" be a real uniformly convex Banach space which admits a weakly sequentially continuous duality mapping from "Equation missing" to "Equation missing", "Equation missing" a nonempty closed convex subset of "Equation missing" which is also a sunny nonexpansive retract of "Equation missing", and "Equation missing" a non-expansive nonself-mapping with "Equation missing". In this paper, we study the strong convergence of two sequences generated by "Equation missing" and "Equation missing" for all "Equation missing", where "Equation missing", "Equation missing" is a real sequence in an interval "Equation missing", and "Equation missing" is a sunny non-expansive retraction of "Equation missing" onto "Equation missing". We prove that "Equation missing" and "Equation missing" converge strongly to "Equation missing" and "Equation missing", respectively, as "Equation missing", where "Equation missing" is a sunny non-expansive retraction of "Equation missing" onto "Equation missing". The results presented in this paper generalize, extend, and improve the corresponding results of Matsushita and Kuroiwa and many others.