  The aim of this paper is to introduce an implicit S-iteration process and
study its convergence in the framework of W-hyperbolic spaces. We show that the
implicit S-iteration process has higher rate of convergence than implicit Mann
type iteration and implicit Ishikawa-type iteration processes. We present a
numerical example to support the analytic result proved herein. Finally, we
prove a data dependence result for a contractive type mapping using implicit
S-iteration process.
