A Novel Four-Step Iteration Scheme With Numerical Examples

Authors

  • Anjali Department of Mathematics, Maharshi Dayanand University, Rohtak 124001, Haryana, India https://orcid.org/0000-0002-6010-6734
  • Seema Mehra Department of Mathematics, Maharshi Dayanand University, Rohtak 124001, Haryana, India https://orcid.org/0000-0001-7219-9387
  • Renu Chugh Department of Mathematics, Gurugram University, Gurugram 122413, Haryana, India

DOI:

https://doi.org/10.26713/cma.v16i3.3206

Keywords:

Banach space, Iterative method, Strong convergence, Order of convergence

Abstract

This study presents a four-step iteration method for approximating the fixed points of a contractive-like mapping. The proposed scheme is conceptually related to classical iterations such as Picard, Mann, and Ishikawa, while extending them in a more general framework. The strong convergence, rate of convergence and stability of the proposed method are established, demonstrating theoretical improvements over existing approaches. Moreover, we present some numerical illustrations to validate our method and these numerical illustrations are compared with some similar schemes available in the literature.

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References

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Published

30-10-2025
CITATION

How to Cite

Anjali, Mehra, S., & Chugh, R. (2025). A Novel Four-Step Iteration Scheme With Numerical Examples. Communications in Mathematics and Applications, 16(3), 909–921. https://doi.org/10.26713/cma.v16i3.3206

Issue

Vol. 16 No. 3 (2025)

Section

Research Article

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