Fuzzy double controlled metric spaces and related results

Abstract

In this paper, we introduce the concept of fuzzy double controlled metric space that can be regarded as the generalization of fuzzy b-metric space, extended fuzzy b-metric space and controlled fuzzy metric space. We use two non-comparable functions α and β in the triangular inequality as: M ( x , z , t α ( x , y ) + s β ( y , z ) ) ≥ M ( x , y , t ) ∗ M ( y , z , s ) . We prove Banach contraction principle in fuzzy double controlled metric space and generalize the Banach contraction principle in aforementioned spaces. We give some examples to support our main results. An application to existence and uniqueness of solution for an integral equation is also presented in this work.

Fuzzy Triple Controlled Metric Spaces and Related Fixed Point Results

“…(iii) Taking η = ν and s + w = t ′ in (m q 4), then our definition reduces to the definition of fuzzy double controlled metric space defined in [33].…”

“…In [31], authors defined fuzzy version of rectangular b-metric space while in [32], Asim et al introduced the concept of extended rectangular b-metric space and proved related fixed point theorem. Recently, Saleem et al [33] introduced the notion of fuzzy double controlled metric space and proved BCMP on such space. Abdeljawad et al [34] modified the definition of controlled metric type space defined in [35] by giving the idea of a double controlled metric type space.…”

On Pentagonal Controlled Fuzzy Metric Spaces with an Application to Dynamic Market Equilibrium

“…Mehmood et al [10] presented fuzzy rectangular b-metric spaces and proved fixed point theorems. Saleem et al [11] coined the notion of fuzzy double controlled metric spaces and proved several fixed point results. Badshah-e-Rome and Sarwar [12] presented the approach of extended fuzzy rectangular b-metric spaces and proved fixed point results for contraction mappings via α-admissibility.…”

“…Expressing α = α/5 + α/5 + α/5 + α/5 + α/5 and by using 3 Journal of Function Spaces (11) and (A1), we obtain…”

Neutrosophic Double Controlled Metric Spaces and Related Results with Application

“…Sezen [13] presented the notion of controlled fuzzy metric spaces and proved various contraction mapping results. Recently, Saleem et al [14] introduced the concept of fuzzy double controlled metric spaces. For related articles, see [15][16][17][18][19][20].…”