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.

We provide a validation of a formal approximate solution to the problem of the evolution of a slowly varying harvested logistic population. Using a contraction mapping proof, we show that the initial value problem for the population has an exact solution lying in an appropriately small neighbourhood of this approximate solution, under quite general conditions.

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.