In this paper, we introduce a new fuzzy contraction mapping and prove that such mappings have fixed point in τ-complete fuzzy metric spaces. As an application, we shall utilize the results obtained to show the existence and uniqueness of random solution for the following random linear random operator equation. Moreover, we shall show the existence and uniqueness of the solutions for nonlinear Volterra integral equations on a kind of particular fuzzy metric space.
AgarwalR.P., BenchohraM. and HamaniS., Boundary value problems for fractional differential equations, Georgian Math J16 (2009), 401–411.
2.
AzamA. and BegI., Common fixed points of fuzzy maps,, Math Comput Model49 (2009), 1331–1336.
3.
BegI. and AbbasM., Invariant approximation for fuzzy nonexpansive mappings,, Math Bohem136(1) (2011), 51–59.
4.
ButnariuD., Fixed point for fuzzy mapping,, Fuzzy Sets Syst7 (1982), 191–207.
5.
ChangS.S., Probabilistic contractor and the solutions for nonlinear equations in Probabilistic normed spaces, Chines Science Bull19 (1990), 1451–1454.
6.
EstruchV.D. and VidalA., A note on fixed fuzzy points for fuzzy mappings, Proceedings of the II Italian-Spanish Congress on General Topology and Its Applications (Italian) (Trieste, 1999), Rend Ist Mat Univ Trieste32(suppl. 2) (2001), 39–45.
7.
FristedtB., GrayL. A modern approach to probability theory, Boston: BirkhÃd’user (1996).
8.
FangJ.X., A note on fixed point theorems of Hadzic, Fuzzy Sets and Systems48(3) (1992), 391–395.
9.
GeorgeA. and VeeramaniP., On some results in fuzzy metric spaces,, J Fuzzy Sets Syst64 (1994), 395–399.
10.
GeorgeA. and VeeramaniP., On some results of analysis for fuzzy metric spaces,, Fuzzy Sets and Systems90(3) (1997), 365–368.
11.
GuptaV. and VermaM., Common fixed points using (ψ, φ)-type contractive maps in fuzzy metric spaces, , Journal of Applied Research and Technology18 (2020), 27–33.
12.
HadzićO., Fixed point theorems for multivalued mappings in some classes of fuzzy metric spaces, Fuzzy Sets and Systems29 (1989), 115–125.
13.
HadzićO., PapE.Fixed Point Theory in Probabilistic Metric Spaces, Mathematics and Its Applications, vol. 536, Kluwer Academic Publishers, Dordrecht, 2001.
14.
HeilpernS., Fuzzy mappings and fixed point theorems,, J Math Anal Appl83(1981), 566–569.
15.
HuangH., Carić.B., DosenovićT., RakićD., BrdarM., Fixed-Point Theorems in Fuzzy Metric Spaces via Fuzzy F-Contraction, Mathematics9 (2021), 641. https://doi.org/10.3390/math9060641.
16.
KilbasA.A. and MarzanS.A., Nonlinear differential equations with the Caputo fractional derivative in the space of continuously differentiable functions, 82–86, 142;, English Translation Differ Equ41 (2005), 84–89.
