THE NEW FASTEST HYBRID ITERATION PROCESS

Abstract

For a class of contractive operators defined on an arbitrary Banach space, it hasbeen shown recently that the Picard-Mann iteration process converges faster than the Picard iteration process. In this paper, we introduce a new hybrid iteration process which can beseen as a  "double Picard " or a hybrid of Picard iteration process with itself. We first givethe convergence analysis of our new iteration process. Thereafter, we prove that the new process converges faster than Picard-Mann iteration process for contractive-like operators in K-normed linear space.