Fixed Point for New Contraction Mapping in Fréchet Space via Fuzzy Structure with Application

Authors

  • Ahmed Jasim Department of Mathematics, College of Computer Science and Mathematics, University of Thi-Qar, Iraq

DOI:

https://doi.org/10.32792/jeps.v15i4.734

Keywords:

Keywords: ϑ-acceptable mapping, ϑ-θ-fuzzy augmented contraction mapping, fuzzy Fréchet space(FF-space).

Abstract

In this article, we introduce a new type of fuzzy contraction mapping in a fuzzy Fréchet space . This type is known as the fuzzy augmented contraction mapping, which is defined by acceptable mapping. We prove that this mapping possesses a fixed point by proving two results under specific conditions. To support our theoretical results, we studied an application that demonstrates the effectiveness of our approach in solving and finding a unique solution to an integral equation.

References

Zadeh, L. A. (1965). Fuzzy sets, information and control. Information and control, 8(3), 338-353.‏ https://doi.org/10.1016/S0019-9958(65)90241-X

Katsaras, A. K., & Liu, D. B. (1977). Fuzzy vector spaces and fuzzy topological vector spaces. Journal of Mathematical Analysis and Applications, 58(1), 135-146.‏ https://doi.org/10.1016/0022-247X(77)90233-5

Jasim, A. G., & Al-Nafie, Z. D. (2021, March). Fréchet Spaces via Fuzzy Structures. In Journal of Physics: Conference Series (Vol. 1818, No. 1, p. 012082). IOP Publishing.‏ DOI 10.1088/1742-6596/1818/1/012082

Jasim, A. G., & Al-Nafie, Z. D. (2021, March). Fuzzy Fréchet Manifold. In Journal of Physics: Conference Series (Vol. 1818, No. 1, p. 012064). IOP Publishing.‏ DOI 10.1088/1742-6596/1818/1/012064

Banach, S. (1922). Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fundamenta mathematicae, 3(1), 133-181.‏ https://eudml.org/doc/213289

Jain, S., & Radenovic, S. (2023). Interpolative fuzzy Z-contraction with its application to Fredholm non-linear integral equation. Gulf Journal of Mathematics, 14(1), 84-98.‏ https://doi.org/10.56947/gjom.v14i1.1009

Jabeen, S., Ur Rehman, S., Zheng, Z., & Wei, W. (2020). Weakly compatible and quasi-contraction results in fuzzy cone metric spaces with application to the Urysohn type integral equations. Advances in Difference Equations, 2020(1), 280.‏ DOI:10.1186/s13662-020-02743-5

Eidi, J. H., Hameed, E. M., & Kider, J. R. (2025). Fixed Point Theorems with its Applications in Fuzzy Complete Convex Fuzzy Metric Spaces. International Journal of Neutrosophic Science (IJNS), 25(3).‏ https://doi.org/10.54216/IJNS.250306

Jasim, A. G., & Al-Nafie, Z. D. (2022, October). Some fixed point theorems in fuzzy Fréchet manifold. In AIP Conference Proceedings (Vol. 2398, No. 1). AIP Publishing.‏ https://doi.org/10.1063/5.0095582

Jasim, A. G., Sangoor, A. A., Mohammed, A. S., Dahess, T. H., & Kamil, A. H. (2024). Common fixed point theorem in fuzzy Fréchet space. Journal of Interdisciplinary Mathematics, 27(4), 843-847.‏ https://doi.org/10.47974/JIM-1881

Jasim, A. G., & Harbi, I. (2025). Advancements in Fixed Point Theory for Fuzzy Normed Spaces Using the Common Limit Range Method with Application. European Journal of Applied Science, Engineering and Technology, 3(2), 185-193.‏ https://doi.org/10.59324/ejaset.2025.3(2).16

Schweizer, B., & Sklar, A. (1960). Statistical metric spaces. Pacific J. Math, 10(1), 313-334.‏ http://dx.doi.org/10.2140/pjm.1960.10.313

Sadeqi, I., & Kia, F. S. (2009). Fuzzy normed linear space and its topological structure. Chaos, Solitons & Fractals, 40(5), 2576-2589.‏ https://doi.org/10.1016/j.chaos.2007.10.051

Downloads

Published

2025-12-01

Issue

Vol. 15 No. 4 (2025): JOURNAL OF EDUCATION FOR PURE SCIENCE

Section

Articles

License

Copyright (c) 2025 Journal of Education for Pure Science

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Copyright Policy

Authors retain copyright of their articles published in the Journal of Education for Pure Science (JEPS).

By submitting their work, authors grant the journal a non-exclusive license to publish, distribute, and archive the article in all formats and media.

License

All articles published in JEPS are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

This license permits unrestricted use, distribution, and reproduction in any medium, provided that the original author(s) and the source are properly credited.

Author Rights

Authors have the right to:

  • Share their articles on personal websites, institutional repositories, and academic platforms

  • Reuse their work in future research and publications

  • Distribute the published version without restriction

Journal Rights

The journal retains the right to:

  • Publish and archive the articles

  • Include them in indexing and archiving systems such as LOCKSS and CLOCKSS

  • Promote and disseminate the published work

Responsibility

The contents of all articles are the sole responsibility of the authors. The journal, editors, and editorial board are not responsible for any errors, opinions, or statements expressed in the published articles.

Open Access Statement

JEPS provides immediate open access to its content, supporting the principle that making research freely available to the public enhances global knowledge exchange.

This work is licensed under a Creative Commons Attribution 4.0 International License.
https://creativecommons.org/licenses/by/4.0/