Approximation of Three-Steps Iterative Schemes in Banach Spaces using Zamfirescu Operator and their Applications

Authors

  • M. A. Adeniyi Department of Mathematics, University of Ilorin, Nigeria.
  • M. O. Fatai Department of Mathematics, Federal University Oye-Ekiti, Nigeria.
  • R. U. Kanu Department of Basic Sciences (Maths), Babcock University, Ilishan-Remo, Nigeria.
  • E. E. Aribike Department of Mathematical Sciences, Lagos State University of Science and Technology, Ikorodu, Lagos, Nigeria.
  • K. Rauf Department of Mathematics, University of Ilorin, Nigeria.

DOI:

https://doi.org/10.63746/njtd.v23i3.4124

Keywords:

Contraction mapping, Convergent rate, Convex metric Space, Uniformly convex Banach space, convex subset, Fixed point iteration

Abstract

: Iterative methods play an important role in fixed point theory and provide effective procedures for approximating fixed points of nonlinear operators. Among the various iterative schemes developed for this purpose, the Noor iteration has attracted considerable attention because of its applicability to a broad class of nonlinear problems. In this study, a modified form of the Noor iterative scheme is introduced with the aim of improving its convergence behavior. The proposed modification is constructed by appropriately altering the Noor iteration while retaining its basic iterative structure. The convergence characteristics of the original Noor iteration and the proposed modified Noor iteration are then investigated and compared. To assess the effectiveness of the proposed scheme, two numerical examples are considered for nonlinear mappings possessing fixed points. The iterative processes are implemented from the same initial approximation and under comparable control parameters, allowing their convergence behaviors to be examined on a common basis. The numerical results demonstrate that the modified Noor iteration approaches the fixed point more rapidly than the original Noor iteration in the examples considered. In particular, the proposed scheme requires fewer iterations to attain a prescribed level of accuracy, indicating an improvement in computational efficiency. These observations provide numerical evidence that the modification enhances the convergence performance of the Noor scheme. The results are therefore useful in the development and analysis of efficient iterative procedures for approximating fixed points of nonlinear operators and related nonlinear problems. The numerical examples used demonstrates faster convergence of the proposed Modified Noor iteration for the nonlinear heat-transfer model considered in this paper.

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Published

2026-09-30

Issue

Vol. 23 No. 3 (2026): Volume 23, Issue 3, September 2026.

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Articles

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