Abstract
In this paper, we study some coincidence point and common fixed point theorems in fuzzy metric spaces by using three-self-mappings. We prove the uniqueness of some coincidence point and common fixed point results by using the weak compatibility of three-self-mappings. In support of our results, we present some illustrative examples for the validation of our work. Our results extend and improve many results given in the literature. In addition, we present an application of fuzzy differential equations to support our work.
Highlights
In 1975, Kramosil and Michalek [2] introduced the notion of fuzzy metric (FM) space, and they compared the concept of fuzzy metric with the statistical metric space and proved that both the conceptions are equivalent in some cases
We proved some generalized unique coincidence points and common fixed point (CFP) theorems for weakly-compatible three self-mappings in FM spaces without the assumption that the “fuzzy contractive sequences are Cauchy.”
The “triangular property of FM” is used as a basic tool throughout the complete paper to get the existence of unique coincidence points and CFP results in FM spaces
Summary
Zadeh [1] introduced the concept of fuzzy sets which is defined as “a set contracted from a function having a domain is a nonempty set Ω and range in 1⁄20, 1 is called a fuzzy set, that is if G : Ω ⟶ 1⁄20, 1.” In 1975, Kramosil and Michalek [2] introduced the notion of fuzzy metric (FM) space, and they compared the concept of fuzzy metric with the statistical metric space and proved that both the conceptions are equivalent in some cases. The concept of rational type fuzzy-contraction is given by Rehman et al [19] They proved some unique FP theorems with the application of nonlinear integral in FM spaces. Jabeen et al. Journal of Function Spaces [21] presented the concept of weakly compatible selfmappings in fuzzy cone metric spaces, and they proved some coincidence point and CFP theorems in the said space with integral type application. We present some illustrative examples and an application of fuzzy differential equation to support our work By using this concept, researchers can prove more coincidence points and CFP results for different contractive type mappings in FM spaces with the application of integral operators.
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