Abstract
In the theory of fuzzy fixed point, many authors have been proved different contractive type fixed point results with different types of applications. In this paper, we establish some new fuzzy cone contractive type unique coupled fixed point theorems (FP-theorems) in fuzzy cone metric spaces (FCM-spaces) by using “the triangular property of fuzzy cone metric” and present illustrative examples to support our main work. In addition, we present a Lebesgue integral type mapping application to get the existence result of a unique coupled FP in FCM-spaces to validate our work.
Highlights
The theory of fuzzy sets was introduced by Zadeh [1]
In 1975, Kramosil and Michalek [2] introduced the concept of fuzzy metric spaces (FM-space); they present some structural properties of FM-space
We have presented an application of the two Lebesgue Integral Equations (LIE) for a common solution to uphold our work
Summary
The theory of fuzzy sets was introduced by Zadeh [1]. Later on, in 1975, Kramosil and Michalek [2] introduced the concept of fuzzy metric spaces (FM-space); they present some structural properties of FM-space. Chen et al [26], in 2020, gave the idea of coupled fuzzy cone contractive-type mappings They proved “some coupled FP-theorems in FCM-spaces with non-linear integral type application.”. Rehman and Aydi [27], in 2021, presented the concept of rational type fuzzy cone contraction mappings in FCM-spaces. They used “the triangular property of fuzzy metric” as a fundamental tool and proved some common FP-theorems and give an application.
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