Best Proximity Point Theorem for φ ̃–ψ ̃-Proximal Contractive Mapping in Fuzzy Normed Space

Authors

Raghad I. Sabri Mathematics and Computer Applications, Department of Applied Sciences, University of Technology, Baghdad, Iraq https://orcid.org/0000-0002-3673-5864
Buthainah A. A. Ahmed Department of Mathematics, College of Sciences, University of Baghdad, Baghdad, Iraq

DOI:

https://doi.org/10.30526/36.3.3080

Keywords:

Fuzzy normed space, φ ̃–ψ ̃-proximal contractive mapping, Best proximity point, Best proximity point theorems, Proximal contractive mapping .

Abstract

The study of fixed points on the maps fulfilling certain contraction requirements has several applications and has been the focus of numerous research endeavors. On the other hand, as an extension of the idea of the best approximation, the best proximity point (ƁƤƤ) emerges. The best approximation theorem ensures the existence of an approximate solution; the best proximity point theorem is considered for addressing the problem in order to arrive at an optimum approximate solution. This paper introduces a new kind of proximal contraction mapping and establishes the best proximity point theorem for such mapping in fuzzy normed space ( space). In the beginning, the concept of the best proximity point was introduced. The concept of proximal contractive mapping in the context of fuzzy normed space is then presented. Following that, the best proximity point theory for this kind of mapping is established. In addition, we provide an example application of the results

References

Banach, S. Sur les opérations dans les ensembles abstraits et leur application aux équations integrals, Fundamenta Mathematicae, 1922, 3, 133–181. DOI: https://doi.org/10.4064/fm-3-1-133-181

Katsaras A. K. Fuzzy topological vector spaces I, Fuzzy Sets and Systems, 1981, 6(1), 85–95. DOI: https://doi.org/10.1016/0165-0114(81)90082-8

Bînzar, T.; Pater, F.; Nădăban, S. A study of boundedness in fuzzy normed linear spaces, Symmetry, 2019, 11(7),923.

Sabri, R. I. Fuzzy convergence sequence and fuzzy compact operators on standard fuzzy normed spaces, Baghdad Science Journal, 2021, 18(4), 1204–1211.

Kider, J. R.; Kadhum, N. A. Properties of Fuzzy Norm of fuzzy Bounded Operators. Iraqi Journal of Science, 2021, 58(3A), 1237–1281.

Bînzar, T.; Pater, F.; Nădăban, S. Fixed-Point Theorems in Fuzzy Normed Linear Spaces for Contractive Mappings with Applications to Dynamic-Programming, Symmetry, 2022, 14(10), 1-12.

Sharma, M.; Hazarika, D. Fuzzy Bounded Linear Operator in Fuzzy Normed Linear Spaces and its Fuzzy Compactness, New Mathematics and Natural Computation, 2020, 16(1), 177-193.

Rassias, J.; Karthikeyan, S.; Ganapathy, G.; Suresh, M.; Kumar, T. Generalized Ulam-Hyers Stability Results of a Quadratic Functional Equation in Felbin’s Type Fuzzy Normed Linear Spaces, International Journal of Analysis and Applications, 2022, 20, 15.

Rana, A.; Buthainah, A.; Fadhel, F. On Fixed Point Theorem in Fuzzy Normed Space, Journal of Al-Nahrain University, 2015, 18(4), 138-143. DOI: https://doi.org/10.22401/JNUS.18.4.19

Nadaban, S.; Dzitac, I. Atomic decompositions of fuzzy normed linear spaces for wavelet applications, Informatica (Netherlands), 2014, 25(4), 643–662. DOI: https://doi.org/10.15388/Informatica.2014.33

Bag, T.; Samanta, S. K. Finite-dimensional fuzzy normed linear spaces, Journal of Fuzzy Mathematics, 2003, 11(3), 687–705.

Vetro, C.; Salimi, P. Best proximity point results in non-archimedean fuzzy metric spaces, Fuzzy Information and Engineering, 2013, 5(4), 417–429. DOI: https://doi.org/10.1007/s12543-013-0155-z