On the strong convergence theorems by the hybrid method for a family of mappings in uniformly convex Banach spaces

Abstract

Some algorithms for nding common xed point of a family of mappings is<br />constructed. Indeed, let C be a nonempty closed convex subset of a uniformly<br />convex Banach space X whose norm is Gateaux di erentiable and let {T_n} be<br />a family of self-mappings on C such that the set of all common fixed points<br />of {T_n} is nonempty. We construct a sequence {x_n} generated by the hybrid<br />method and also we give the conditions of {T_n} under which {x_n} converges<br />strongly to a common xed point of {T_n}.