On Extended b -Rectangular and Controlled Rectangular Fuzzy Metric-Like Spaces with Application

Abstract

In this article, we introduce the notions of extended b -rectangular and controlled rectangular fuzzy metric-like spaces that generalize many fuzzy metric spaces in the literature. We give examples to justify our newly defined fuzzy metric-like spaces and prove that these spaces are not Hausdorff. We use fuzzy contraction and prove Banach fixed point theorems in these spaces. As an application, we utilize our main results to solve the uniqueness of the solution of a differential equation occurring in the dynamic market equilibrium.

Exploring Fuzzy Triple Controlled Metric Spaces: Applications in Integral Equations

“…In conclusion, we established that the operator T possesses a fixed point, denoted as η * ∈ C([0, 1], R), which serves as a solution to integral Equation (20). Therefore, all the conditions of Theorem 1 have been satisfied.…”

“…Subsequently, in 2019, Mehmood et al proceeded to introduce the concept of fuzzy rectangular b-metric spaces [19]. Expanding upon these concepts, Saleem et al introduced the notion of extended rectangular fuzzy b-metric spaces and established fixed point results in their work [20]. Additionally, in [21], Saleem et al introduced the concept of fuzzy double controlled metric spaces and demonstrated the application of the Banach contraction mapping principle in this context.…”

Coincidence Point of Edelstein Type Mappings in Fuzzy Metric Spaces and Application to the Stability of Dynamic Markets

“…The fixed point theory has numerous applications in various disciplines like science, engineering and economics; see, e.g., [16][17][18][19]. In particular, the stability of dynamic markets can be identified by the equilibrium point (price), and the equilibrium point is considered as a fixed point of some particular function associated with the demand and supply at successive stages of the market (see, e.g., [20][21][22] and the references therein).…”