Fixed Point for New Contraction Mapping in Fréchet Space via Fuzzy Structure with Application
DOI:
https://doi.org/10.32792/jeps.v15i4.734الكلمات المفتاحية:
Keywords: ϑ-acceptable mapping, ϑ-θ-fuzzy augmented contraction mapping, fuzzy Fréchet space(FF-space).الملخص
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.
المراجع
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
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