CONVERGENCE AND STABILITY OF FIBONACCI SR-ITERATION PROCESS FOR MONOTONE NON-LIPSCHITZIAN MAPPING

Abstract

In this paper, we introduce a new iteration process (called the Fibonacci SR-iterationprocess) for monotone non-Lipschitzian mapping (that is, nearly asymptotically nonexpansive mapping) in partially ordered hyperbolic metric space and prove strong and Δ-convergence theorem. Further, we construct a numerical example to demonstrate thatour iteration process is faster than the Fibonacci Mann iteration process [4]. Our results generalize, extend, and unify the corresponding results of Agrawal et. al. [3, 4], Alfuraidan and Khamsi [5], and many more results in this direction.