In this paper, we propose a new definition of INTUITIONISTIC FUZZY quasi-METRIC and pseudo-METRIC SPACES based on INTUITIONISTIC FUZZY points. We prove some properties of intuitionist FUZZY quasi- METRIC and pseudo-METRIC SPACES, and show that every intuitionist FUZZY pseudo-METRIC space is intuitionist FUZZY regular and INTUITIONISTIC FUZZY completely normal and hence INTUITIONISTIC FUZZY normal. These are the INTUITIONISTIC FUZZY generalization of the corresponding properties of FUZZY quasi-METRIC and pseudo- METRIC SPACES.

In this paper, we introduce INTUITIONISTIC FUZZY contraction mapping and prove a fixed point theorem in INTUITIONISTIC FUZZY METRIC SPACES.

Based on previous results that study the completion of FUZZY METRIC SPACES, we show that every INTUITIONISTIC FUZZY quasi-METRIC space, using the notion of FUZZY METRIC space in the sense of Kramosil and Michalek to obtain a generalization to the quasi-METRIC setting, has a bicompletion which is unique up to isometry.

In this paper, we introduce a new class of implicit functions and also common property (E.A) in modified INTUITIONISTIC FUZZY METRIC SPACES and utilize the same to prove some common fixed point theorems in modified INTUITIONISTIC FUZZY METRIC SPACES besides discussing related results and illustrative examples. We are not aware of any paper dealing with such implicit functions in modified INTUITIONISTIC FUZZY METRIC SPACES.

The concept of summability plays a central role in finding formal solutions of partial differential equations. In this paper, we introduce the concept of Cesàro summability in an INTUITIONISTIC FUZZY $n$-(NORMED) linear space (IFnNLS). We show that Cesàro summability method is regular in an IFnNLS, but  Cesàro summability does not imply usual convergence in general. Further, we search for additional conditions under which the converse holds.

Approach to FUZZY differential equations in FUZZY metrics using generalized contraction theorems One of the most fascinating fields of mathematical inquiry is fixed point. In this direction, by utilizing ”the triangular property of FUZZY METRIC ”, we investigate certain special common fixed point solutions for a pair of self mappings without continuity on FUZZY METRIC SPACES under the generalized contra ction requirements. We also provide generalized Ciri’s contraction theorems and weak contraction theorems. The findings are corroborated by pertinent cases. Additionally, we provide a workable application of the FUZZY differential equation s to guarantee the presence of a singular common solution to support our primary research.

This paper deals with some issues of common fixed point theory involving two different types of INTUITIONISTIC FUZZY contractive mappings. INTUITIONISTIC FUZZY Jungck's common fixed point theorem (see, [1]) with respect to contraction defined in [8] and INTUITIONISTIC FUZZY Pant's common fixed point theorem (see, [2]) for y-f weakly commuting mappings are proved.