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Peer-reviewedCC BY 4.0Axioms

Existence and Approximation of Fixed Points for a Novel Class of Mappings with Applications

  • Rida Zainab1
  • Mujahid Abbas1,2,3
  • Muhammad Waseem Asghar2
  1. 1Department of Mathematics, Government College University Lahore, Lahore 54000, Pakistan
  2. 2Department of Mechanical Engineering Science, University of Johannesburg, Johannesburg 2092, South Africa
  3. 3Department of Medical Research, China Medical University, Taichung 40604, Taiwan
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Abstract

In this paper, we introduce a new and more general class of mappings that extends the Suzuki-type nonexpansive mapping. We first establish the existence of fixed points for this new class of mappings. Then, we propose an iterative scheme to approximate the fixed point and prove its convergence, rate of convergence, and data dependence results. A numerical example is presented to demonstrate the effectiveness of the proposed iterative scheme. Finally, we apply our results to solve boundary value problems, illustrating the practical usefulness of the proposed approach.

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Cite

BibTeXRIS
BibTeX
@article{zainab2026existence,
  title = {{Existence and Approximation of Fixed Points for a Novel Class of Mappings with Applications}},
  author = {Rida Zainab and Mujahid Abbas and Muhammad Waseem Asghar},
  journal = {Axioms},
  year = {2026},
  month = oct,
  doi = {10.3390/axioms15100730},
  url = {https://www.mdpi.com/2075-1680/15/10/730},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Existence and Approximation of Fixed Points for a Novel Class of Mappings with Applications
AU  - Rida Zainab
AU  - Mujahid Abbas
AU  - Muhammad Waseem Asghar
PY  - 2026
DA  - 2026/10/01
JO  - Axioms
DO  - 10.3390/axioms15100730
UR  - https://www.mdpi.com/2075-1680/15/10/730
AB  - In this paper, we introduce a new and more general class of mappings that extends the Suzuki-type nonexpansive mapping. We first establish the existence of fixed points for this new class of mappings. Then, we propose an iterative scheme to approximate the fixed point and prove its convergence, rate of convergence, and data dependence results. A numerical example is presented to demonstrate the effectiveness of the proposed iterative scheme. Finally, we apply our results to solve boundary value problems, illustrating the practical usefulness of the proposed approach.
SN  - 2075-1680
ER  -