A NOVEL FOUR-STEP ITERATION SCHEME WITH NUMERICALS

Authors

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. We also consider the strong convergence, order of convergence and stability of the proposed method.
Moreover, we present some numerical illustrations to validate our method and these numerical illustrations have
been compared with some similar schemes available in the literature.

Downloads

Download data is not yet available.

References

J. Li, Applications of fixed point theory to generalized Nash equilibria of nonmonetized noncooperative

games on Banach lattices, Nonlinear Analysis Forum 18 (2013), 1-11.

R. M. Danet and M. V. Popescu, Some applications of the fixed-point theory in economics, Creative Mathe-

matics and Informatics 17(3) (2008), 392-398.

S. Mehra, R. Chugh, S. Haque and N. Mlaiki, Iterative algorithm for solving monotone inclusion and fixed

point problem of a finite family of demimetric mappings, AIMS Mathematics 8(8) (2023), 19334-19352.

R. Chugh and C. Batra, Fixed point theorems of enriched Ciric’s type and enriched Hardy-Rogers contractions

Numerical Algebra, Control and Optimization 15(2) (2025), 459-481.

´E. Picard, Dissertation on the theory of partial differential equations and the method of successive approxi-

mations, Journal of Pure and Applied Mathematics 6 (1890), 145-210.

W. R. Mann, Mean value methods in iteration, Proceedings of the American Mathematical Society 4(3)

(1953), 506-510.

S. Ishikawa, Fixed points by a new iteration method, Proceedings of the American Mathematical Society

(1) (1974), 147-150.

V. Kanwar, P. Sharma, I. K. Argyros, R. Behl, C. Argyros, A. Ahmadian and M. Salimi, Geometrically

constructed family of the simple fixed point iteration method, Mathematics 9(6) (2021), 694.

Anku, M. Narang and V. Kanwar, On Some Fixed Point Iterative Schemes with Strong Convergence and

Their Applications, Mathematical and Computational Applications 28(2) (2023), 45.

P. Sharma, H. Ramos, R. Behl and V. Kanwar, A new three-step fixed point iteration scheme with strong

convergence and applications. Journal of Computational and Applied Mathematics 430 (2023), 115242.

C. O. Imoru and M. O. Olatinwo, On the stability of Picard and Mann iteration processes, Carpathian Journal

of Mathematics 19(2) (2003), 155-160.

M. O. Osilike, Stability results for fixed point iteration procedures, Journal of the Nigerian Mathematical

Society 14(15) (1995) 17-29.

V. Berinde and F. Takens, Iterative approximation of fixed points, 1912 (2007), Berlin: Springer.

A. M. Harder, Fixed point theory and stability results for fixed point iteration procedures (1988).

V. Berinde, Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators,

Fixed Point Theory and Applications 2004 (2004) 97–105.

V. Berinde, On the stability of some fixed point procedures, Buletinul s, tiint, ific al Universitatii Baia Mare,

Seria B, Fascicola matematic˘a-informatic˘a XVIII(1) (2002), 7-14.

X. Weng, Fixed point iteration for local strictly pseudo-contractive mapping, Proceedings of the American

Mathematical Society 113(3) (1991), 727-731.

Published

19-02-2026

How to Cite

Anjali, Mehra, S., & Chugh, R. (2026). A NOVEL FOUR-STEP ITERATION SCHEME WITH NUMERICALS. Communications in Mathematics and Applications, 16(3). Retrieved from https://www.rgnpublications.com/journals/index.php/cma/article/view/3206

Issue

Vol. 16 No. 3 (2025)

Section

Research Article

License

Creative Commons Licence 4.0 by  

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.