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A note on a faster fixed point iterative method
  • Krushnachandra Panigrahy,
  • Debasisha MishraOrcid
Krushnachandra Panigrahy
National Institute of Technology Raipur
Author Profile
Debasisha Mishra
Orcid
National Institute of Technology Raipur
Author Profile

Peer review status:UNDER REVIEW

01 Jun 2020Submitted to Mathematical Methods in the Applied Sciences
06 Jun 2020Assigned to Editor
06 Jun 2020Submission Checks Completed
07 Jun 2020Reviewer(s) Assigned
07 Jul 2020Review(s) Completed, Editorial Evaluation Pending

Abstract

In this paper, we introduce an iteration process to approximate a fixed point of a contractive self-mapping. The comparison theorem indicates that our iteration process is faster than the other existing iteration processes in the literature. We also obtain convergence and stability theorems of this iterative process for a contractive self-mapping. Numerical examples show that our iteration process for approximating a fixed point of a contractive self-mapping is faster than the existing methods. Based on this process, we finally present a new modified Newton-Raphson method for finding the roots of a function and generate some nice polynomiographs.