Fixed Points Results for $(\alpha, \beta)$ - Contractive Mapping in Intuitionistic Fuzzy Metric-Like Spaces

Year 2025, Volume: 13 Issue: 2 , 160 - 169 , 31.10.2025

Banu Pazar Varol , Şuara Onbaşıoğlu Altuhovs

https://izlik.org/JA63DA92WB

Abstract

Onbasioglu and Pazar Varol [17] successfully unified metric-like and intuitionistic fuzzy metric structures and establish a foundation for significant advances in fixed-point theory through their introduction of intuitionistic fuzzy metric-like spaces. Building upon this work, we propose a novel class of contraction mappings, called $(\alpha, \beta)$-contraction mappings, within these spaces. Moreover, we contribute to the expanding knowledge base by presenting innovative results related to sequence convergence within this novel framework. We introduce a new concept, namely the $1-\mathcal{M-}$ Cauchy sequence and $1-\mathcal{M-}$ completeness within intuitionistic fuzzy metric-like spaces.

Keywords

intuitionistic fuzzy (\alpha, \beta) contractive mapping, , 1 −M−complete intuitionistic fuzzy metric-like spaces , fixed point

References

• [1] Alaca C, Turkoglu D, Yildiz C. Fixed points in intuitionistic fuzzy metric spaces, Chaos, Solitons and Fractals, 29, 1073–8, 2006.
• [2] Atanassov K. T., Intuitionistic fuzzy sets, Fuzzy sets and Systems, 20, 87-96, 1986.
• [3] Aygun H., Guner E., Minona J., Valero O., Fuzzy partial metric spaces and fixed point theorems, Mathematics, 10(17), 2022.
• [4] Din F. U., Javed K., Ishtiaq U.,Ahmed K.,Arshad M., Park C., Existence of fixed point results in neutrosophic metric-like spaces. AIMS Mathematics, 7(9): 17105–17122, 2022.
• [5] George A., Veeramani P., On some result in fuzzy metric spaces, Fuzzy Sets and Systems, 64, 395-399, 1994.
• [6] George A., Veeramani P., Some theorems in fuzzy metric spaces, The Journal of Fuzzy Mathematics 3, 933–940, 1995.
• [7] Grabiec M., Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27, 385–389. 1988.
• [8] Gregori V., Sapena A., On fixed-point theorems in fuzzy metric spaces, Fuzzy Sets and Systems 125, 245–252, 2002.
• [9] Gregori V., Lopez-Crevillen A., Morillas S., Sapena A., On convergence in fuzzy metic spaces, Topology and its Applicaitions, 156, 3002-3006, 2009.
• [10] Gregori V., Morillas S. and Sapena A., Examples of fuzzy metrics and applications, Fuzzy Sets and Systems 170, 95-111, 2011.
• [11] Gregori V., Minana J., Miravet D., Extended Fuzzy Metrics and Fixed Point Theorems, Mathematics, 7(3), 303, 2019.
• [12] Harandi A. A., Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory Appl., Article ID 204, , 1-10, 2012.
• [13] Hussain A., Sulami H. A., Ishtiaq U., Some new aspects in the intuitionistic fuzzy and neutrosophic fixed point theory. Journal of Function Spaces, 2022, 3138740, 14 pages, 2022.
• [14] Ishtiaq U., S¸ims¸ek N., Javed K., Ahmed K., Uddin F., Kiris¸ci M., Fixed point theorem for neutrosophic extended metric-like spaces and their application. Sigma J Eng Nat Sci, Vol. 41, No. 4, pp. 750-757, August, 2023.
• [15] Kramosil O., J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika, 11, 326-334, 1975.
• [16] Mihet D., A Banach contraction theorem in fuzzy metric spaces, Fuzzy Sets and Systems 144, 431 – 439, 2004.
• [17] Onbasioglu Suara, Pazar Varol B., Intuitionistic Fuzzy Metric-like Spaces and Fixed-Point Results, Mathematics, vol.11 (1902), pp. 1-15, 2023.
• [18] O¨ ner T., Shostak A., Some remarks on fuzzy sb-metric spaces, Mathematics, 8, 2123, doi:10.3390/math8122123, 2020.
• [19] Park J.H., Intuitionistic fuzzy metric spaces, Chaos, Solitons and Fractals, 22, 1039-1046, 2004.
• [20] Pazar Varol B., Statistically Convergent Sequences in Intuitionistic Fuzzy Metric Spaces, Axioms, 11(4), 1-7, 2022.
• [21] Priskillal J.J., Thangavelu P., (2017), Intuitionistic Fuzzy (y;n)-Contractive Mapping and Fixed Points, Journal of Analysis and Number Theory, vol.5 (2), pp. 105-108.
• [22] Rafi M., Noorani M. S. M., Fixed theorems on intuitionistic fuzzy metric space, Iran. J. Fuzzy Syst., 3, 23–29, 2006.
• [23] Schweizer B., Sklar v., Statistical metric spaces, Pacific J. Math., 10, 313-334, 1960.
• [24] Shostak A., George- Veeramani Fuzzy Metrics Revised, Axioms, 7(3), 60, 2018.
• [25] Shukla S., M. Abbas, Fixed point results in fuzzy metric-like spaces, Iran. J. Fuzzy Syst., 11 (2014).
• [26] Shukla S., Gopal D., Sintunavarat W., A new class of fuzzy contractive mappings and fixed point theorems, Fuzzy Sets and Systems, 350, 85–94, 2018.
• [27] Sintunavarat W., Kumam P., Fixed point theorems for a generalized intuitionistic fuzzy contraction in intuitionistic fuzzy metric spaces, Thai J. Math., 10, 123–135, 2012.
• [28] Turkoglu D., Alaca C, Cho Y.J. and Yıldız C., Common fixed point theorems in intuitionistic fuzzy metric spaces, J. Appl. Math and Computing, 22(1-2), 411-424, 2006.
• [29] Uddin F., Ishtiaq U., Saleem N., Ahmad K., Jarad F., Fixed point theorems for controlled neutrosophic metric-like spaces. AIMS Mathematics, 7(12): 20711–20739, 2022.
• [30] Zadeh L. A., Fuzzy sets. Inform Control, 8, 338–53, 1965.