In this paper, we establish common fixed point theorem for type(β) compatible four mappings with implicit relations defined on an intuitionistic fuzzy metric space. Also, we present the example of common fixed point satisfying the conditions of main theorem in an intuitionistic fuzzy metric space.

Most mathematical theories start from humble beginnings where a mathematician while examining some mathematical object makes fundamental, but ad hoc, observations. When the significance of these observations are realized some organised study begins during which these are explored in detail for some central examples. In this second part of theory building some general themes of investigation are...

The aim of this paper is to introduce the notion of  -chainable intuitionistic fuzzy metric spaces and prove a common fixed point theorem for four weakly compatible mappings in this newly defined space. Our result is intuitionistic fuzzy version of Cho and Jung's [1] and Mukherjee's [9] results in  -chainable fuzzy metric space.

Menger called a finitely-compact metric space in which any two distinct points are contained in exactly one set congruent to a euclidean straight line a straight-line space (S.L. space) [ l ] . 1 He observed that in such spaces a segment (or vector) addition can be defined in a very simple way (see §2 of the present paper) which satisfies all requirements for an abelian group except, in general...

In this paper, we introduce intuitionistic fuzzy contraction mappingand prove a fixed point theorem in intuitionistic fuzzy metric spaces.