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

Authors

  • Jong Kyu Kim Department of Mathematics Education, Kyungnam University
  • Rashmi Verma Department of Applied Mathematics, Shri Shankaracharya Institute of Professional Management and Technology
  • Samir Dashputre
  • 　 Padmavati Department of Mathematics, Govt. V.Y.T. Autonomous P.G. College

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.

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Published

2025-02-25

Issue

Volume 30, Number 1, March 2025

Section

Articles