Compatible Maps and Compatible Maps of Types (Α) and (Β) in Intuitionistic Fuzzy Metric Spaces

Abstract

Abstract. In this paper, we first formulate the definition of compatible maps and compatible maps of types (a) and (/3) in intuitionistic fuzzy metric spaces and give some relations between the concepts of compatible maps and compatible maps of types (a) and 03).

Coupled Fixed Point Theorem for Weakly Compatible Mappings in Intuitionistic Fuzzy Metric Spaces

“…For basic definitions and structure on intuitionistic fuzzy metric spaces we refer to [1][2][3][4][5][6].However we give some definitions in the sequel. Then (M, N) is called an intuitionistic fuzzy metric on X. the functions M(x, y, t) and N(x, y, t) denote the degree of nearness and the degree of non-nearness between x and y with respect to t, respectively.…”

“…Motivated by the idea of intuitionistic fuzzy metric sets Park [8] introduced the concept of intuitionistic fuzzy metric spaces using continuous t-norms and continuous t-conorms. Later on , many authors [2][3][4][5][6] have studied fixed points results in intuitionistic fuzzy metric spaces.Fang [7] defined -contractive conditions and proved some important fixed point theorems under -contractions for compatible and weakly compatible maps in Menger PM-spaces using t-norm of H-type introduced by Hadzic [9]. In this paper , first we introduce the notion of t-conorm of Htype analogous to t-norm of H-type introduced by Had c [9] and using this notion we prove a common coupled fixed point theorem for compatible mappings in intuitionistic fuzzy metric spaces.…”

Common fixed point theorem for subcompatible maps of type (α) in weak non-Archimedean intuitionistic fuzzy metric space

“…For instance Turkoglu et.al. [16] introduced compatible maps and compatible maps of types (α) and (β) in intuitionistic fuzzy metric spaces. Further, they proved common fixed point theorems for compatible maps.…”

Some Fixed Point Theorems in intuitionistic fuzzy metric spaces

“…Turkoglu et al [31] introduced the concept of compatible maps and compatible maps of types (α) and (β) in intuitionistic fuzzy metric spaces and gave some relations between the concepts of compatible maps and compatible maps of types (α) and (β).…”