Path Convergence and Approximation of Common Zeroes of a Finite Family of m-Accretive Mappings in Banach Spaces

Abstract EN

Let E be a real Banach space which is uniformly smooth and uniformly convex.

Let K be a nonempty, closed, and convex sunny nonexpansive retract of E, where Q is the sunny nonexpansive retraction.

If E admits weakly sequentially continuous duality mapping j, path convergence is proved for a nonexpansive mapping T:K→K.

As an application, we prove strong convergence theorem for common zeroes of a finite family of m-accretive mappings of K to E.

As a consequence, an iterative scheme is constructed to converge to a common fixed point (assuming existence) of a finite family of pseudocontractive mappings from K to E under certain mild conditions.