A New Composite General Iterative Scheme for Nonexpansive Semigroups in Banach Spaces

Throughout this paper we denoted by and the set of all positive integers and all positive real numbers, respectively. Let X be a real Banach space, and let C be a nonempty closed convex subset ofX. Amapping T ofC into itself is said to be nonexpansive if ‖Tx−Ty‖ ≤ ‖x−y‖ for each x, y ∈ C. We denote by F T the set of fixed points of T . We know that F T is nonempty ifC is bounded; for more detail see 1 . A one-parameter familyS {T t : t ∈ } from C of X into itself is said to be a nonexpansive semigroup on C if it satisfies the following conditions: