Common fixed point theorems for families of compatible mappings in intuitionistic fuzzy metric spaces

Abstract

In this paper, we prove some common fixed point theorems for any even number of compatible mappings in complete intuitionistic fuzzy metric spaces. Our main results extend and generalize some known results in fuzzy metric spaces and intuitionistic fuzzy metric spaces.

Prevalent fixed point theorems on MIFM-Spaces using the ( C L R S R ) property and implicit function

“…In 2004, Park [36] suggested the notion of intuitionistic fuzzy metric spaces (IFMS), which is a generalization of George and Veeramani's fuzzy metric space [15]. Many authors have recently proven fixed point theorems in IFMS ( [2,3,6,20,35,38,40,42,44]).…”

Common Fixed Point Theorems for Weakly Subsequentially Continuous Mappings in Modified Intuitionistic Fuzzy Metric Spaces

“…Later Ç oker [6] introduced a topology on intuitionistic fuzzy sets. Park [21] introduced the notion of intuitionistic fuzzy metric spaces as a generalization to fuzzy metric spaces, which is a combination between intuitionistic fuzzy sets and the concept of a fuzzy metric space given by George and Veeramani [9], many authors established some results concerning fixed point in such spaces, see for example [2,5,12,14,19,29]. Meanwhile, jungck [16] defined the concept of compatible mappings, Jungck and Roadhes [17] generalized the last concept to the weakly compatible mappings, which is weaken than the compatible ones.…”

(φ, ψ)-weak contractions in intuitionistic fuzzy metric spaces

“…Indeed, Park defined a Hausdorff topology on this kind of intuitionistic fuzzy metric spaces and showed that every metric induces an intuitionistic fuzzy metric. This result motivated many authors to study and investigate fixed point results in intuitionistic fuzzy metric (and normed) spaces (see, for examples, [1,3,7,9,20,22,31,34,35,40]). Since the intuitionistic fuzzy metric space has extra conditions, Saadati et al [38] modified the idea of intuitionistic fuzzy metric space and obtained various fixed point results in modified intuitionistic fuzzy metric spaces.…”