Path convergence and approximation of common zeroes of a finite family of \(m\)-accretive mappings in Banach spaces (Q1957566)

Summary: 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 \(T:K\rightarrow K\). As an application, we prove strong convergence to 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.