Composite Halpern Iteration for Approximating Common Zero of a Finite Family of m-Accretive Mappings
Yun Cheng · Journal of Civil Aviation University of China · 2009
This paper introduces a new composite halpern iteration process for approximating common zero points of m-accretive mappings in Banach spaces.Suppose K is a closed convex subset of a strictly convex real Banach space E which has a uniformly Gateaux differentiable norm.Suppose that every nonempty closed convexˇ bounded subset of E has the fixed point property for nonexpansive mappings.Ai ∶ K→E(i=1,2,…,r)is a family of m-accretive mappings from K to E,{xn} is a sequence defineded by composite Halpern iteration.Then as n→∞,{xn} converges strongly to a common solution of the equations Ai x=0(i=1,2,…,r).