Common Fixed Point Results in Fuzzy b-Metric Space Using the Integrals as Application
Keywords:
Fuzzy b-Metric Space ; Common Fixed Point; Convergent Sequence; Compatible Mapping; Integral EquationAbstract
In recent years, the notion of fuzzy mathematics has become one of the interesting field of research. In this article, using the idea of fuzzy b-metric space and contraction mappings, we prove Banach contraction theorem. Also applying the idea of different compatible mappings, unique common fixed point results in fuzzy b-metric space are introduced and these results are connected in terms of the integral as the application. Some interesting instances to highlight the significance of our research are presented. Previous findings from the pertinent study are presented as lemmas and corollaries. Our findings complement and add to a large number of existing findings
Downloads
References
1] A. George, and P. Veeramani, On Some Results in Fuzzy Metric Spaces, Fuzzy sets and systems, 64(1994), 395-399.
[2] A. L. Zadeh, Fuzzy Sets, Information and Control, 8(1965), 338-353.
[3] B. Schweizer and A. Sklar, Statistical Metric Spaces,Pacific J. Math., 10(1), (1960), 385-389.
[4] C. D. Bari, and C. Vetro , Fixed Points, Attractors and Weakfuzzy Contractive Mappings in a Fuzzy Metric Space, Journal of Fuzzy Mathematics, 1(2005), 973–982. Mathematics. 8, (2020), 59-67, https://doi.org/10.3390/math8122123.
[5] G. Mani, J. Arul, G. Prakasam, H. Absar, A. Imran, and C. Park, On Solution of Fredholm Integral Equations via Fuzzy b-Metric Spaces Using Triangular Property, AIMS Math., 7(2022), 11102–11118.[CrossRef]
[6] G. Mani, A. Joseph, L. Guran, and R. George, Some Results in Fuzzy b-Metric Space With b-Triangular Property and Applications to Fredholm Integral Equations and Dynamic Programming, P Mathematics, 11(2023), 1-17. https://doi.org/10.3390/math11194101.
[7] I. Altun, Some Fixed Point Theorems for Single and Multi Valued Mappings on Ordered Nonarchimedean Fuzzy Metric Spaces, Iranian Journal of Fuzzy Systems, 7(2007), 91–96.
[8] I. Bakhtin, The contraction mapping principle in almost metric spaces, Funct. Anal., 30(1998), 26–37.
[9] I. Kramosil and J. Michlek, Fuzzy Metric and Statistical Metric Spaces, Kybernetika, 11(1975), 336–344.
[10] J. Y. Cho, Common fixed points of compatible maps of type (B) on fuzzy metric spaces, Fuzzy Sets and Systm, 93, (1998), 99-111.
[11] M. Grabiec, Fixed Points in Fuzzy Metric Spaces, Fuzzy sets and systems, 27(1988), 385-389.
[12] R. Saif, U. Sichuan, and C. Ronnason, Rational Type Fuzzy-Contraction Results in Fuzzy Metric Spaces with an Application, Wiley Journal of Mathematics, (2021), 1-13, DOI:10.1155/2021/6644491.
[13] S. Nadaban, Fuzzy b-metric spaces, International Journal of Computers Communications and Control, 11(2016), 273–281.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Mr. Thaneshor Bhandari, Dr. KB Manandhar, Prof. Dr. Kanhaiya Jha
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
