Some iterative method for finding a common zero of a finite family of accretive operators in Banach spaces

Abstract

‎The purpose of this paper is to introduce a new mapping for a finite‎ ‎family of accretive operators and introduce an iterative algorithm‎ ‎for finding a common zero of a finite family of accretive operators‎ ‎in a real reflexive strictly convex Banach space which has a‎ ‎uniformly G^ateaux differentiable norm and admits the duality‎ ‎mapping $j_{varphi}$‎, ‎where $varphi$ is a gauge function invariant‎ ‎on $[0,infty)$‎. ‎Furthermore‎, ‎we prove the strong convergence under‎ ‎some certain conditions‎. ‎The results obtained in this paper improve‎ ‎and extend the corresponding ones announced by many others‎.