Rational type intuitionistic fuzzy soft contraction results and application to integral problem

Pooja Dhawan; Tripti Sharma

doi:10.5269/bspm.76855

Pooja Dhawan Maharishi Markandeshwar Engineering College, MM (DU), Mullana, Ambala-133207
Tripti Sharma

Abstract

This work aims to present the concept of intuitionistic fuzzy soft contraction maps of rational type in intuitionistic fuzzy soft metric spaces (IFSMS). With thorough examples to support our outcomes, we provide some fixed point findings in IFSMS under rational type intuitionistic fuzzy soft contraction conditions. Additionally, we incorporate an application to solve a nonlinear integral problem for a unique solution in order to assist our efforts.

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References

Agarwal, R.P., Hussain, N. and Taoudi, M.A., Fixed point theorems in ordered Banach spaces and applications to nonlinear integral equations, Abstract and Applied Analysis. 245–872, (2012).

Atanassov, K.T., Intuitionistic fuzzy sets, Fuzzy Sets and Systems. 20,87–96, (1986).

Ahmad J. and Arshad, M., On multi-valued contraction in cone metric spaces without normality, The Scientific World Journal. 2013, (2013).

Bari, C.D. and Vetro, C., Fixed points, attractors and weak fuzzy contractive mappings in a fuzzy metric space, Journal of Fuzzy Mathematics. 1, 973-982, (2005).

Beaula, T. and Gunaseeli, C. On fuzzy soft metric spaces, Malaya Journal of Mathematics. 2(3), 197–202, (2014).

Banach, S., Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fundamenta Mathematicae. 3, 133–181, (1922).

Bakhtin, I.A., The contraction mapping principle in quasi metric spaces, Functional Analysis. 30, 26–37, (1989).

Covitz, H. and Nadler, S.B.,Multi-valued contraction mappings in generalized metric spaces, Israel Journal of Mathematics, 8, 5–11, (1970).

Das, S. and Samanta, S., Soft metric, Ann. Fuzzy Math. Inform, 6(1), 77–94, (2013).

Dhawan, P. and Grewal, A.,Some novel fixed point findings in Intuitionistic Fuzzy b-Metric Spaces, Lecture Notes in Networks and Systems, Springer book series. 5 (2024).

Dhawan, P., Gupta, V., Kaur, J., Existence of coincidence and common fixed points for a sequence of mappings in Quasi partial metric spaces, Journal of Analysis. 30, 405–414, (2022).

Dhawan, P., Kaur, J., Some common fixed point theorems in ordered partial metric spaces via F-generalized contractive type mappings, Mathematics. 7(2), 193, (2019).

Frechet, M.M., Sur quelques points du calcul fonctionnel, Rendiconti Del Circolo Matematico di Palermo. 22(1), 1–72, (1906).

Gregori, V. and A. Sapena, On fixed-point theorems in fuzzymetric spaces, Fuzzy Sets and Systems, 125, 245–252, (2002).

Gupta, V., Dhawan, P., Verma, M., Some novel fixed point results for (Ω, ∆)-weak contraction condition in complete fuzzy metric spaces, Pesquisa Operacional, 43, 1–20, (2023).

Hussain, N. and Toudi, M.A., Krasnoselskii-type fixed point theorems with application Volterra integral equations, Fixed Point theory and Applications. 1, 1–16, (2013).

Molodtsov, D., Soft set theory First results, Computers and Mathematics with Applications. 37, 19–31, (1999).

Park, J.H., Intuitionistic fuzzy metric spaces, Chaos Solitons Fractals. 22, 1039–1046, (2004).

Rehman, S.U., Chinnram, R.and Boonpok, C., Rational type fuzzy contraction mappings in fuzzy metric spaces, Journal of mathematics. (2021).

Rusmiari, N., Putra, D. and Sasmita, A. Fuzzy logic method for evaluation of diffculty level of exam and student graduation, International Journal of Computer Science. 10(2), 223–229, (2013).

Schweizer, B. and Sklar, A. Statical metric spaces, Pacific Journal of Mathematics. 10, 314–334, (1960).

Siva Naga Malleswari, V. and Amarendra Babu, V., Intuitionistic fuzzy soft metric spaces, AIP Conference Proceedings. 2246, (2020).

Nadler, S.B., Multi-valued contraction mappings, Pacific Journal of Mathematics. 30, 475–488, (1969).

Zadeh, L.A., Fuzzy sets, Inf. Control. 8, 338–353, (1965).