Harmonic function is one of an important branches of complex analysis. The first study of complex valued, harmonic mappings defined on a domain D was given by ClunIe and SheIl-Small [1]. Harmonic functions have been studied by different researchers such as Silverman [6]. In the present paper, a new class of harmonic univalent functions will be introduced. Various properties of functions belong to this class which include coefficient bounds, growth bounds, a closure property, extreme points, neighborhood and a convex combination will be obtained.

The division algorithm for multivariate polynomials over fields has been introduced not very long ago, in connection with algorithmic and computational problems in the rings since the work of Buchberger. The well-known fact is a term order must be a well-ordering and the division procedure in the ring of multivariate polynomials over a field terminates even if the division term is not leading term, but is freely chosen. In this paper, we will show the original geometric approach to the classification of all possible orders on the ring of polynomials in two variables is given. The connection between this classification and the well-known classification of Robiano is exposed in details.

The theory of operators is an important subject in analytic function theory, geometric function theory and univalent function theory. It also is an important subject in applied sciences. It is still an active field of research and various types of problems, which can be solved by generalising operators. Recently, many researchers have shown great interests in the study of differential operators in the theory of univalent functions and various subclasses of analytic functions defined in the open unit disc. In this paper a generalised derivative operator will be used to derive some results concerning the subordination and superordination of analytic function in the open unit disc.

The object of the present paper is to derive some results on differential subordination associated with a generalized derivative operator for certain normalized analytic functions in the open unit disc. The authors establish sandwich type theorems. These results extend many previously known results.

The object of the present paper is to introduce a new subclass of p-valent starlike functions with negative coefficients in the open unit disc which is defiined by a generalized derivative operator. We obtain coefficient inequalities, growth and distortion theorems and extreme points for the subclass of p-valent functions.

The aim of this paper is to introduce and study a new class of Bazilevič p-valent function of order β by using the subordination concept between this function and a generalized derivative operator. Some interesting properties are also obtained

The theory of analytic functions and more specific p-valent functions, is one of the most fascinating topics in one complex variable. There are many remarkable theorems dealing with extremal problems for a class of p-valent functions on the unit disk U. Recently, many researchers have shown great interests in the study of differential operator. The objective of this paper is to define a new generalized derivative operator of p-valent analytic functions of fractional power in the open unit disk U. This operator generalized some well-known operators studied earlier, we mention some of them in the present paper. Motivation by the generalized derivative operator; we introduce and investigate two new subclasses of starlike p-valent analytic functions of fractional power with positive coefficients and starlike p-valent analytic functions of fractional power with negative coefficients, respectively. In addition, a sufficient condition will be obtained. Some corollaries are also pointed out. Moreover, we determine the extreme points of functions belong to the class.

The aim of the article is to study a sufficient condition for the classes of starlike and convex harmonic univalent functions with respect to k- symmetric points. The necessary condition for f to be in the classes will be studied. In addition, growth bounds for functions will also be given.

In this paper, we study and introduce the majorization properties of a new class of analytic p-valent functions of complex order defined by the generalized hypergeometric function. Some known consequences of our main result will be given. Moreover, we investigate the coefficient

estimates for this class.

In the present investigation, new subclasses of analytic functions in the open unit disk which are defined using generalized derivative operator are introduced. Several interesting properties of these classes are obtained.

The aim of this paper is to determine the Fekete-Szegö inequalities for a normalized analytic function defined on the open unit disk lies in a region starlike with respect to 1 and it is symmetric with respect to the real axis by using the operator given recently by the authors. As a special case of this result, Fekete-Szegö inequality for a class of functions defined by fractional derivatives is also obtained.

Using a generalized derivative operator, we introduce and study a new class of harmonic univalent functions. In the present paper, we investigate some results for functions f belong to this class which include the necessary and sufficient coefficient bounds. Growth bounds and a closure property are also obtained.

Motivated by generalized derivative operator defined by the authors (El-Yagubi and Darus, 2013) and the technique of differential subordination, several interesting properties of the operator are given.

The aim of this paper is to introduce a new class of analytic functions in the unit disk, with negative coefficients, via a new generalized derivative operator. We prove coecient inequalities for the new class of functions and for a subclass of it, as well as distortion theorems for functions in this subclass and for their derivatives. We determine the extreme points of the newly introduced subclass.

In the present paper, the coefficient estimate of a class of funtions starlike with respect to k-symmetric points defined by generalised derivative operator will be studied. The integral representation and several coefficient inequalities of functions belonging to this class will be given.

In the present paper, two new subclasses of analytic functions with respect to k-symmetric points defined by differential operator. Some interesting properties belonging to these classes are provided.

A new generalised derivative operator is introduced. This operator generalised many well-known operators studied earlier by many authors. New subclasses of analytic functions in the open unit disc are introduced which are defined using generalized derivative operator. Inclusion theorems are investigated for functions to be in the classes. Furthermore, generalised Bernardi-Libera-Livington integral operator is shown to be preserved for these classes.

In this paper, the definition of intuitionistic fuzzy parameterised fuzzy soft set (ifpfs-sets) is introduced with their properties. Two operations on intersection are introduced. Also, some examples for these operations are given. The ifpfs-set, namely union and definition of ifpfs-aggregation operator which forms ifpfs-decision making method is Introduced.