Strong Convergence of a Modified Halpern's Iteration for Nonexpansive Mappings (Fixed Point Theory and Applications, 2009)
The purpose of this paper is to consider that a modified Halpern's iterative sequence {xn} converges strongly to a fixed point of nonexpansive mappings in Banach spaces which have a uniformly Gâteaux differentiable norm. Our result is an extension of the corresponding results.