On Z*-open, Z*-closed functions

Journal of Advanced Studies in Topology, 2012

The purpose of this paper is to introduce some new classes of functions by using b-open sets. We investigate some of their fundamental properties and the connections between these functions and other known existing topological functions are studied.

Main aim of this article is the discussion of Univalent complex functions, Cap like complex functions, and star like complex functions, close-to-cap like complex functions.

Proyecciones (Antofagasta), 2009

In this paper, we introduce and study the notions of θ-generalizedsemi-open function, θ-generalized-semi-closed function,pre-θ-generalizedsemi-open function,pre-θ-generalized-semi-closed function, contra preθ-generalized-semi-open,contra pre-θ-generalized-semi-closed function and θ-generlized-sem-homeomorphism in topological spaces and study their properties.

Proyecciones (antofagasta), 2009

In this paper, we introduce and study the notions of θ-generalizedsemi-open function, θ-generalized-semi-closed function,pre-θ-generalizedsemi-open function,pre-θ-generalized-semi-closed function, contra preθ-generalized-semi-open,contra pre-θ-generalized-semi-closed function and θ-generlized-sem-homeomorphism in topological spaces and study their properties.

In this paper, we introduce and study the notion of generalized Z-closed sets. Also, the notion of generalized Z-open sets and some of its basic properties are introduced discussed. Further, we introduce the notion of generalized Z-closed functions. Moreover, some characterizations and properties of it are investigated.

2013

A new class of generalized open sets, called z-open sets which are weaker than both θ-semiopen sets and θ-preopen sets defined by Altunöz and Aslım [2], is introduced and some properties are obtained by Özkoç [14]. In this paper in order to investigate some different properties we introduce two strong form of z-open sets called z-regular sets and z-θ-open sets. By means of z-θ-open sets we also introduce a new class of functions called strongly θ-z-continuous functions which is a generalization of strongly θ-precontinuous functions. We obtain some characterizations and several properties of such functions. Moreover, we define strongly z-closed graphs, z-regular spaces and z-T2 spaces and investigate the relationship between their properties and strongly θ-z-continuous functions. Mathematics Subject Classification: Primary 54C08, 54C10

The aim of this paper we introduce Z-irresolute, Z-open, Zclosed, pre-Z-open and pre-Z-closed mappings and investigate properties and characterizations of these new types of mappings.

A subclass A (n, k) of analytic functions f (z) in the unit disc U is considered. By means of the result due to K. Sakaguchi (J. Math. Soc. Japan 11(1959), 72-75) for f (z) ∈ A (1, 1), some generalization properties of f (z) ∈ A (n, k) with several applications are discussed.

In the present paper we introduce and studied two subclasses of multivalent functions denoted by M λ p,n (γ;β ) and N λ p,n (μ,η;δ ) . Further, by giving specific values of the parameters of our main results, we will find some connection between these two classes, and moreover, several consequences of main results are also discussed.

Acta Universitatis Sapientiae: Mathematica, 2017

By making use of new linear fractional differential operator, we introduce and study certain subclasses of analytic functions associated with Symmetric Conjugate Points and defined in the open unit disk U = {z : |z| < 1}. Inclusion relationships are established and convolution properties of functions in these subclasses are discussed.