Volume 31, No. 1 (2021)

ALPHA GENERALIZED PRECLOSED SETS IN INTUITIONISTIC FUZZY TOP-OLOGICAL SPACES

JYOTI PANDEY BAJPAI(1), S.S. THAKUR(2) and ALPA SINGH RAJPUT(3)

The concept of intuitionistic fuzzy set was introduced by Atanassov as a generalization of fuzzy sets. In 1997 Coker introduced the concept of intuitionistic fuzzy topological spac-es. In 2008, Thakur introduced the notion of intuitionistic fuzzy generalized closed set in intuitionistic fuzzy topological space. Several authors studied in various forms of intui-tionistic fuzzy g-closed set and related topological properties. The aim of this paper is to introduce the new class of intuitionistic fuzzy closed sets called intuitionistic fuzzy αgp closed sets in intuitionistic fuzzy topological space. The class of all intuitionistic fuzzy αgp- closed sets lies between the class of all intuitionistic fuzzy α-closed sets and class of all intuitionistic fuzzy gspr-closed sets. We also introduce the concepts of intuitionistic fuzzy αgp open sets, intuitionistic fuzzy αgp- continuous mappings in intuitionistic fuzzy topological spaces.

FUZZY TOPOLOGICAL PROPERTIES OF SPACES AND FUNCTIONS WITH RESPECT TO THE frwg-CLOSURE OPERATOR

ANJANA BHATTACHARYYA

We study the frwg-closure operator in fuzzy topological spaces, investigating the corresponding notions of regular, normal, compact, T2-space and various classes of functions-closed, open, continuous, irresolute, strongly continuous, weakly continuous. We establish connections between the above-mentioned properties of functions and the properties of fuzzy topological spaces.

A COMMON FIXED POINT APPROACH FROM NON-ARCHIMEDEAN MENGER SPACES TO MODULAR METRIC SPACES VIA SIMULATION FUNCTION

BHAVANA DESHPANDE

In this paper, we prove common fixed point theorems on non-Archimedean Menger spac-es by using the concept of simulation function. We also deduce some consequences in modular metric spaces.

A CHARACTERIZATION OF 0-COMPLETENESS IN PARTIAL METRIC SPACES

SUSHANTA KUMAR MOHANTA(1) and PRIYANKA BISWAS(2)

In this paper, we introduce the concept of p-point in a partial metric space and extend Weston’s characterization of metric completeness to partial metric spaces in terms of p-point. As a consequence of this study, we obtain the celebrated Banach Contraction Principle in the framework of 0-complete partial metric spaces.

A UNIFIED FORM OF SEPARATION AXIOMS IN IDEAL TOPOLOGICAL SPACES

TAKASHI NOIRI(1) and VALERIU POPA(2)

We introduce the notion of mIO(X)-structures determined by operators Int, Cl and Cl⋆ on an ideal topological space (X, τ, I). By using mIO(X)-structures, we obtain a unified form of some separation axioms containing semi-I-Ti, β-I-Ti, b-I-Ti (i = 0, 1, 2) and other.

ON SOME WEAKER FORMS OF HUREWICZ PROPERTY IN BITOPOLOGICAL SPACES

RITU SEN

We introduce mildly Hurewicz property in the setting of bitopological spaces and study this concept along with that of almost Hurewicz property introduced by A. E. Eysen and S. Özcağ in [4]. Some connections between these properties and Hurewicz property are highlighted. We investigate the preservation of almost Hurewicz property and of mildly Hurewicz property under various types of mappings between bitopological spaces.

NEW SUBCLASSES OF ANALYTIC FUNCTIONS RELATED TO QUASI-CONVEX FUNCTIONS

GAGANDEEP SINGH(1) and GURCHARANJIT SINGH(2)

This paper deals with the study of certain new subclasses of analytic functions related to quasi-convex functions in the open unit disc. We establish some geometric properties such as the coefficient estimates, distortion theorems and growth theorems for these classes. The results proved earlier will follow as special cases.

CHARACTERIZATIONS OF COUNTABLY ρI- COMPACT IDEAL TOPOLO GICAL SPACES

SUMIT MITTAL(1) and B. K. TYAGI(2)

The concept of countably ρI- compactness is introduced and several characterizations of this notion are obtained. It is shown that an ideal space (X, τ, I ) is countably ρI -compact if and only if every countable locally finite modulo I, with I ∈ I, the family of non-ideal sets is finite.