One of the most active and developing fields in both pure and applied mathematics is the theory of fixed points. It is possible to formulate a large number of nonlinear issues that arise in many scientific domains as fixed point problems. Since Zadeh first introduced the concept of fuzzy mathematics in 1965, the interest in fuzzy metrics has grown to the point that several studies have concentrated on examining their topological characteristics and applying them to mathematical issues. This was primarily because, in certain situations, fuzziness rather than randomization was the cause of uncertainty in the distance between two spots. Many mathematicians have examined and developed the concept of distance in relation to fuzzy frameworks because it is a naturalist concept. Generally speaking, it is impossible to determine the precise distance between any two locations. Thus, we deduce that if we measure the same distance between two locations at different times, the results will differ. There are two approaches that can be used to manage this situation: statistical and probabilistic. But instead of employing non-negative real numbers, the probabilistic approach makes use of the concept of a distribution function. Since fuzziness, rather than randomness, is the cause of the uncertainty in the distance between two places. Because of the positive real number b ≥ 1, the area of fuzzy b-metric space is larger than fuzzy metric space. Thus, this field is the source of our concern. This study aims to use the notion of compatible mappings and semicompatible mappings of type (A) to develop some common fixed point theorems in fuzzy b- metric space. A few ramifications of our primary discovery are also provided. Included are pertinent examples to highlight the importance of these key findings. Our results add to a number of previously published findings in the literature.
| Published in | Pure and Applied Mathematics Journal (Volume 13, Issue 6) |
| DOI | 10.11648/j.pamj.20241306.13 |
| Page(s) | 100-108 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
Fuzzy b-Metric Space, Compatible Mappings, Common Fixed Point
| [1] | Bakhtin, I., The contraction mapping principle in almost metric spaces, Funct. Anal., 1989, 30, 26-37. |
| [2] | Czerwik, S., Contraction mappings in b-metric spaces, Inform. Univ. Ostrav,1993, 1, 5-11. |
| [3] | Cho, Y. J., Kang S. M. & Jung J. S., Common fixed points of compatible maps of type β on fuzzy metric spaces, Fuzzy Sets and Systems, 1989, 93, 99-108. |
| [4] | George, A. & Veeramani, P., On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 1994, 64, 395-399. |
| [5] | Grabiec, M., Fixed points in fuzzy metric spaces, Fuzzy sets and systems, 1983, 27, 385-389. |
| [6] | Jungck, G., Compatible mapping and Common fixed points, Internat. J. Math. and math. Sci., 1986, 9(4), 771-779. |
| [7] | Jungck G., Murthy, P.P. & Cho,Y. J., Compatible mappings of type (A) and common fixed points, Math. Japon., 1993, 38, 381-390. |
| [8] | Jungck G. & Rhoades, B. E., Fixed Point for Set Valued functions without Continuity, Indian J. Pure Appl. Math., 1998, 29(3), pp. 771-783. |
| [9] | Manandar, k. B., Jha, K. & Porru, G, Common fixed point theorem of compatible mapping s of type (K) in fuzzy metric spaces, /journals/EGMMA, ISSN:2090-729 (online), 2014, 2(2), 248-253. |
| [10] | Kramosil, I. & Michlek J., Fuzzy metric and statistical metric spaces, Kybernetika, 1975, 11, 336-344. |
| [11] | Nadaban, S., Fuzzy b-metric spaces, International Journal of Computers Communications and Control, 2016, 11, 273-281. |
| [12] | Pathak, H. K., Cho, Y. J. & Kang, S. M., Compatible mappings of type (P) and fixed point theorem in metric spaces and Probabilistic metric spaces, Novi Sad J. Math., 1996, 26(2), 87-109. |
| [13] | Schweizer, B. & Sklar, A., Statistical metric spaces,Pacific J. Math., 1960, 10(1), 385-389. |
| [14] | Sedagi, S. & Shobe, N., 2012, Common fixed point theorem in b-fuzzy metric space, Nonlinear Functional Analysis and Applications, 2012 17, 349-359. |
| [15] | Singh, Bijedra & Chauhan, M. S., Common fixed points of compatible maps in fuzzy metric spaces,Fuzzy Sets and Systems, 2000, 115, 471-475. |
| [16] | Yumnam, R., Common fixed point theorems of compatible mappings of type (A) in fuzzy metric spaces, IJRAR Research Journal, 2011, 5(6): 307-316. |
| [17] | Zadeh, A. L., Fuzzy Sets, Information and Control, 1965, 8, 338-353. |
APA Style
Bhandari, T., Manandhar, K. B., Jha, K. (2024). Fixed Point Theorem in Fuzzy b-Metric Space Using Compatible Mapping of Type (A). Pure and Applied Mathematics Journal, 13(6), 100-108. https://doi.org/10.11648/j.pamj.20241306.13
ACS Style
Bhandari, T.; Manandhar, K. B.; Jha, K. Fixed Point Theorem in Fuzzy b-Metric Space Using Compatible Mapping of Type (A). Pure Appl. Math. J. 2024, 13(6), 100-108. doi: 10.11648/j.pamj.20241306.13
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Download@article{10.11648/j.pamj.20241306.13,
author = {Thaneshor Bhandari and Kanchha Bhai Manandhar and Kanhaiya Jha},
title = {Fixed Point Theorem in Fuzzy b-Metric Space Using Compatible Mapping of Type (A)},
journal = {Pure and Applied Mathematics Journal},
volume = {13},
number = {6},
pages = {100-108},
doi = {10.11648/j.pamj.20241306.13},
url = {https://doi.org/10.11648/j.pamj.20241306.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20241306.13},
abstract = {One of the most active and developing fields in both pure and applied mathematics is the theory of fixed points. It is possible to formulate a large number of nonlinear issues that arise in many scientific domains as fixed point problems. Since Zadeh first introduced the concept of fuzzy mathematics in 1965, the interest in fuzzy metrics has grown to the point that several studies have concentrated on examining their topological characteristics and applying them to mathematical issues. This was primarily because, in certain situations, fuzziness rather than randomization was the cause of uncertainty in the distance between two spots. Many mathematicians have examined and developed the concept of distance in relation to fuzzy frameworks because it is a naturalist concept. Generally speaking, it is impossible to determine the precise distance between any two locations. Thus, we deduce that if we measure the same distance between two locations at different times, the results will differ. There are two approaches that can be used to manage this situation: statistical and probabilistic. But instead of employing non-negative real numbers, the probabilistic approach makes use of the concept of a distribution function. Since fuzziness, rather than randomness, is the cause of the uncertainty in the distance between two places. Because of the positive real number b ≥ 1, the area of fuzzy b-metric space is larger than fuzzy metric space. Thus, this field is the source of our concern. This study aims to use the notion of compatible mappings and semicompatible mappings of type (A) to develop some common fixed point theorems in fuzzy b- metric space. A few ramifications of our primary discovery are also provided. Included are pertinent examples to highlight the importance of these key findings. Our results add to a number of previously published findings in the literature.},
year = {2024}
}
TY - JOUR T1 - Fixed Point Theorem in Fuzzy b-Metric Space Using Compatible Mapping of Type (A) AU - Thaneshor Bhandari AU - Kanchha Bhai Manandhar AU - Kanhaiya Jha Y1 - 2024/12/18 PY - 2024 N1 - https://doi.org/10.11648/j.pamj.20241306.13 DO - 10.11648/j.pamj.20241306.13 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 100 EP - 108 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.20241306.13 AB - One of the most active and developing fields in both pure and applied mathematics is the theory of fixed points. It is possible to formulate a large number of nonlinear issues that arise in many scientific domains as fixed point problems. Since Zadeh first introduced the concept of fuzzy mathematics in 1965, the interest in fuzzy metrics has grown to the point that several studies have concentrated on examining their topological characteristics and applying them to mathematical issues. This was primarily because, in certain situations, fuzziness rather than randomization was the cause of uncertainty in the distance between two spots. Many mathematicians have examined and developed the concept of distance in relation to fuzzy frameworks because it is a naturalist concept. Generally speaking, it is impossible to determine the precise distance between any two locations. Thus, we deduce that if we measure the same distance between two locations at different times, the results will differ. There are two approaches that can be used to manage this situation: statistical and probabilistic. But instead of employing non-negative real numbers, the probabilistic approach makes use of the concept of a distribution function. Since fuzziness, rather than randomness, is the cause of the uncertainty in the distance between two places. Because of the positive real number b ≥ 1, the area of fuzzy b-metric space is larger than fuzzy metric space. Thus, this field is the source of our concern. This study aims to use the notion of compatible mappings and semicompatible mappings of type (A) to develop some common fixed point theorems in fuzzy b- metric space. A few ramifications of our primary discovery are also provided. Included are pertinent examples to highlight the importance of these key findings. Our results add to a number of previously published findings in the literature. VL - 13 IS - 6 ER -
Department of Mathematics, Butwal Multiple Campus, Tribhuvan University, Kathmandu, Nepal; Department of Mathematics, School of Science, Kathmandu University, Dhulikhel, Nepal
Department of Mathematics, School of Science, Kathmandu University, Dhulikhel, Nepal
Department of Mathematics, School of Science, Kathmandu University, Dhulikhel, Nepal
