Halit Orhan

ON A SUBCLASS OF CERTAIN STARLIKE FUNCTIONS WITH NEGATIVE COEFFICIENTS

A certain subclass T›(n;p;‚;fi)of starlike functions in the unit disk is introduced. The object of the present paper is to derive several interesting properties of functions belonging to the class T›(n;p;‚;fi): Coe-cient inequalities, distortion the- orems and closure theorems of functions belonging to the class T›(n;p;‚;fi) are determined. Also we obtain radii of convexity for the class T›(n;p;‚;fi): Furthermore, integral operators and modi- fled Hadamard products of several functions belonging to the class T›(n;p;‚;fi) are studied here.

Starlikeness and Convexity of Generalized Struve Functions

We give sufficient conditions for the parameters of the normalized form of the generalized Struve functions to be convex and starlike in the open unit disk.

Fekete-Szego Problem for a Generalized Subclass of Analytic Functions

In this present work, the authors obtain Fekete-Szego inequality for certain normalized analytic function f(z) dened on the open unit disk for which (1 )z(D m ; f(z)) 0 +z (D m+1 ; f(z)) 0 (1 )D m ; f(z)+D m+1 ; f(z) ( 0; m 2 N0; 0) lies in a region starlike with respect to 1 and is symmetric with respect to the real axis. Also certain applications of the main result for a class of functions dened by Hadamard product (or convolution)

Some general univalence criteria for a family of integral operators

The main object of the present paper is to discuss some extensions of univalence conditions for a family of integral operators. Several other closely-related results are also considered. Many known univalence conditions are shown to follow upon specializing the parameters involved in our main results.

Radii of starlikeness of some special functions

Geometric properties of the classical Lommel and Struve functions, both of the first kind, are studied. For each of them, there different normalizations are applied in such a way that the resulting functions are analytic in the unit disc of the complex plane. For each of the six functions we determine the radius of starlikeness precisely.

Coefficient inequalities and inclusion relations for some families of analytic and multivalent functions

Abstract By means of the derivative operator of order m ( m ∈ N 0 ), we introduce and investigate two new subclasses of p -valently analytic functions of complex order. The various results obtained here for each of these two function classes include coefficient inequalities and inclusion relationships involving the ( n , δ ) -neighborhood of p -valently analytic functions. Relevant connections with some other recent investigations are also pointed out.

Differential Subordinations Involving Generalized Bessel Functions

In this paper our aim is to present some subordination and superordination results, using an operator, which involves the normalized form of the generalized Bessel functions of first kind. These results are obtained by investigating some appropriate classes of admissible functions. We obtain also some sandwich-type results, and we point out various known or new special cases of our main results.

Second Hankel determinant for bi-starlike and bi-convex functions of order β

In the present investigation the authors obtain upper bounds for the second Hankel determinant H2(2) of the classes bi-starlike and bi-convex functions of order β, represented by S ? * ( β ) and K?(β), respectively. In particular, the estimates for the second Hankel determinant H2(2) of bi-starlike and bi-convex functions which are important subclasses of bi-univalent functions are pointed out.

SOME NOTES ON EXTENSIONS OF BASIC UNIVALENCE CRITERIA

The object of the present paper is to obtain a more general condition for univalence of analytic functions in the open unit disk U: The signicant relationships and relevance with other results are also given. A number of known univalent conditions would follow upon specializing the parameters involved in our main results.

Fekete-Szegö problem for strongly starlike functions associated with generalized hypergeometric functions

In this paper, we consider the Fekete-Szego problem for strongly starlike functions of order @b defined by the Dziok-Srivastava linear operator.