Naval Singh,
Umashankar Singh,
Ruchi Singh,
- Professor Govt. Dr. SPM Science & Commerce College, Bhopal Madhya Pradesh India
- Associate Professor Sagar Institute of Research & Technology Excellence, Bhopal Madhya Pradesh India
- Professor Department of Mathematics, Pandit S.N. Shukla University, Shahdol, Madhya Pradesh India
Abstract
The purpose of this study is to extend some previously established fixed point results for interval valued fuzzy metric space. For this objective, various contractive criteria with respect to an intimate mapping are applied. We employ intimate mapping in interval valued fuzzy metric space (IVFMS) to validate some well-known fixed point results. Our findings complement and generalize the recent findings of the common fixed point theorem for intimate mapping. The primary aim of this study is to build upon and extend the existing fixed point results within the realm of interval-valued fuzzy metric spaces (IVFMS). Fixed point theorems are crucial in various mathematical and applied fields, providing solutions to equations where a function maps a point to itself. In this research, we focus on applying diverse contractive conditions specifically in the context of intimate mappings to achieve our objectives. Intimate mapping, a relatively novel concept in IVFMS, plays a key role in our analysis. By employing this type of mapping, we are able to verify and validate several well-established fixed point results within IVFMS. This approach not only supports the known results but also broadens their applicability, thereby enhancing the theoretical foundation of fixed point theorems in fuzzy metric spaces. Our findings make significant contributions by complementing and generalizing recent discoveries related to the common fixed point theorem for intimate mappings. In essence, this study provides a deeper and more comprehensive understanding of fixed point theorems, showcasing the versatility and robustness of intimate mappings in interval-valued fuzzy metric spaces. This advancement opens new avenues for future research and potential applications in various scientific and engineering disciplines where fuzzy metric spaces are utilized.
Keywords: Interval-valued fuzzy metric, Fixed point, Common fixed point, Intimate mappings. Contractive condition
[This article belongs to Recent Trends in Mathematics(rtm)]
References
- Kramosil I, Michálek J. Fuzzy metrics and statistical metric spaces. Kybernetika. 1975;11(5):336-44.
- Osman MA. Fuzzy metric space and fixed fuzzy set theorem. Bull. Malaysian Math. Soc. 1983;6(1):1-4.
- Singh B, Jain S. Semicompatibility and fixed point theorems in fuzzy metric space using implicit relation. International Journal of Mathematics and Mathematical Sciences. 2005 Oct;2005(16):2617-29.
- George A, Veeramani. On some results in fuzzy metric space, Fuzzy sets and systems. 1994;64: 395-399.
- Sharma S. Common fixed point theorems in fuzzy metric spaces. Fuzzy sets and systems. 2002 May 1;127(3):345-52.
- Zadeh LA. The concept of a linguistic variable and its application to approximate reasoning—I. Information sciences. 1975 Jan 1;8(3):199-249.
- Jungck G, Murthy PP, Cho YJ. Compatible mappings of type (A) and common fixed points.
- Sahu DR, Dhagat VB, Srivastava M. Fixed points with intimate mappings (I). Bull. Calcutta Math. Soc. 2001;93(2):107-14.
- Li C. Distances between interval-valued fuzzy sets. InNAFIPS 2009-2009 Annual Meeting of the North American Fuzzy Information Processing Society 2009 Jun 14 (pp. 1-3). IEEE.
- Deshmukh V, Jadon BP, Singh R, Malhotra SK. Fixed Point Results on Interval-Valued Fuzzy Metric Space using notation of Pairwise Compatible Maps and Occasionally Weakly Compatible Maps with Application. Asian Research Journal of Mathematics. 2023 Oct 31;19(11):104-14.
- Popa V. A general common fixed point theorem of Meir and Keeler type for noncontinuous weak compatible mappings. Filomat. 2004 Jan 1:33-40.
- Kaleva O, Seikkala S. On fuzzy metric spaces. Fuzzy sets and systems. 1984 Apr 1;12(3):215-29.
- Sharma S, On Fuzzy Metric space, Southeast Asian Bulletin of Mathematics. 2002; 26: 133-145.
- Bonuga V, Veladi S. Some fixed point results in fuzzy metric space using intimate mappings. Ratio Mathematica. 2023;47.
- Shrivastava R and verma . On common fixed point for intimate mapping in fuzzy metric space. International journal of Theoretical & Applied Science. 2016; 8(1): 81-94.
- Cho YJ, Pathak HK, Kang SM, Jung JS. Common fixed points of compatible maps of type (β) on fuzzy metric spaces. Fuzzy sets and systems. 1998 Jan 1;93(1):99-111.
- Yadav D.S and Thakur S.S. Common Fixed Point for R-Weakly Commuting Mapping in Fuzzy 2-Metric spaces. Int. J. Contemp. Math. Sci. 2013;8 (13): 609-614.
- Wadhwa K, Dubey H, Jain R. Impact of EA Like property on common fixed point theorems in fuzzy metric spaces. Journal of Advanced Studies in Topology. 2012 Jul 1;3(1):52-9.
- Shen Y, Li H, Wang F. On interval-valued fuzzy metric spaces. International Journal of Fuzzy Systems. 2012 Jan;14(1):35-44.
- Jha K, Popa V, Manandhar KB. Common fixed points theorem for compatible of type (K) in metric space. Int. J. Math. Sci. Eng. Appl. 2014;89:383-91.
- Kutukcu S, Sharma S, Tokgoz H. A fixed point theorem in fuzzy metric spaces. Int. Journal of Math. Analysis. 2007;1(18):861-72.
- Singh MR, Singh YM. Compatible mappings of type (E) and common fixed point theorems of Meir-Keeler type. Int. J. Math. Sci. Engg. Appl. 2007;1(2):299-315.
- Wadhwa K, Choudhari S, Bohare P. Common Fixed Point Theorems using Common EA Like Property in Fuzzy Metric Space. International Journal of Mathematics Trends and Technology-IJMTT. 2019;65.
- Dolas U. A Common Fixed point theorem in Fuzzy Metric space using E.A like property. Ultra Scientist.2016; 28(1):1-6.
- Singh U.S and Singh N. Common fixed point theorem for rational expression in fuzzy metric space. Journal of the Gujarat research society. 2019; 21(14)
Volume | 01 |
Issue | 01 |
Received | June 25, 2024 |
Accepted | July 6, 2024 |
Published | September 5, 2024 |