The generalized fixed point theorem in fuzzy metric spaces and its application to an integral equation
Abstract
This paper presents a generalized fixed-point theorem in fuzzy metric spaces using an implicit relation to unify different contraction types. Based on continuous t-norms, the result extends previous work and includes corollaries demonstrating its generality. The approach simplifies analysis by eliminating separate proofs for each contraction type, while an application to integral equations demonstrates its practical utility, guaranteeing existence and uniqueness of solutions under specific conditions.
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References
A. George, P. Veeramani, On some results in fuzzy metric spaces. Fuzzy Sets and Systems, vol. 64, pp. 395–399 (1994).
M. Grabiec, Fixed points in fuzzy metric spaces. Fuzzy Sets Syst. 27, 385–389 (1988).
O. Hadzic, A fixed point theorem in Menger spaces. Publ. Inst. Math. (Belgr.), vol. 20, pp. 107–112 (1979).
O. Hadzic, E. Pap, Fixed Point Theory in Probabilistic Metric Spaces. Kluwer Academic, Dordrecht (2001).
O. Kramosil, J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica 11 326–334 (1975).
S.N. Mishra, N. Sharma, S. L. Singh,Common Fixed Points of Maps on Fuzzy Metric Spaces, Internat. J. Math. and Math. Sci., Vol. 17, No. 2, 253-258 (1994).
E. P. Klement, R. Mesiar, E. Pap, Triangular Norms. Trends in Logic, vol. 8. Kluwer Academic, Dordrecht (2000).
D. Rakic, T. Dosenovic, Z.D Mitrovic, M. de la Sen, S. Radenovic, Some fixed point theorems of Ciric type in fuzzy metric spaces. Mathematics, 8(2), 297 (2020).
L. J. Rodriguez, S. Romaguera, The Hausdorff fuzzy metric on compact sets, Fuzzy Sets and Systems, 147, 2, 273-283 (2004).
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