Approximation of a zero point of accretive operator in Banach spaces

This paper introduces a composite iteration scheme for approximating a zero point of accretive operator in the framework of uniformly smooth Banach spaces and the reflexive Banach space which has a weak continuous duality map, respectively. Strong convergence of the composite iteration scheme {x(n)} defined by [GRAPHICS] where J(rn) is the resolvent of m-accretive operator A and it G C is an arbitrary (but fixed) element in C and sequences {alpha(n)} in (0, 1), {beta(n)} in [0, 1] is established. Under certain appropriate assumptions on the sequences {alpha(n)}, {beta(n)} and {r(n)}, that {x(n)} defined by the above iteration scheme converges to a zero point of A is proved. The results improve and extend results of T.H. Kim, H.K. Xu and some others. (c) 2006 Elsevier Inc. All rights reserved.