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

Abstract

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 $T:K\to K$. 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.