Strong Convergence Theorem for Some Nonexpansive-Type Mappings in Certain Banach Spaces

Charles E. Chidume, Abubakar Adamu, Lois C. Okereke

Abstract

Let E be a uniformly convex and uniformly smooth real Banach space with dual space E^*. A new class of relatively J-nonexpansive maps, T : E → E^* is introduced and studied. A strong convergence theorem for approximating a common J-fixed point of a countable family of relatively Jnonexpansive maps is proved. An example of a countable family of relatively J-nonexpansive maps with a non-empty common J-fixed point is constructed. Finally, a numerical example is presented to show that our algorithm is implementable.