Hüseyin Irmak

Fractional calculus and certain starlike functions with negative coefficients

Abstract A certain subclass T ( n , p , λ , α ) 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 , λ , α ). Various distortion inequalities for fractional calculus of functions in the class T ( n , p , λ , α ) are also given.

Coefficient bounds for some families of starlike and convex functions of complex order

Abstract In the present work, the authors determine coefficient bounds for functions in certain subclasses of starlike and convex functions of complex order, which are introduced here by means of a family of nonhomogeneous Cauchy–Euler differential equations. Several corollaries and consequences of the main results are also considered.

Neighborhoods for certain subclasses of multivalently analytic functions defined by using a differential operator

In the present investigation, by making use of the familiar concept of neighborhoods of analytic and multivalent functions, we derive coefficient bounds and distortion inequalities, associated inclusion relations for the (n,@d)-neighborhoods of subclasses of analytic and multivalent functions with negative coefficients, which are defined by means of a certain nonhomogenous differential equation. Several special cases of the main results are mentioned.

A subclass of analytic functions defined by using certain operators of fractional calculus

Making use of certain operators of fractional calculus, we introduce a new class F6(n,A,a) of functions which are analytic in the open unit disk /4 and obtain a necessary and sufficient condition for a function to be in the class Fs(n,A, ct). We also determine the radii of close-to-convexity, starlikenees, and convexity. Finally, an application involving fractional calculus of functions in the class F6(n, A, a) is considered.

A certain subclass of analytic functions involving operators of fractional calculus

Making use of certain operators of fractional calculus, we introduce a new class Tμ(n,λ,α) of functions which are analytic and univalent in the open unit disk u and obtain a necessary and sufficient condition for a function to be in the class Tμ(n,λ,α). The various other results presented here for the class Tμ(n,λ,α) include the radii of close-to-convexity, starlikeness, and convexity, and some growth and distortion theorems involving fractional integrals and fractional derivatives. Some interesting consequences and possible further generalizations of these results are also pointed out.

Some relations between certain classes consisting of α-convex type and Bazilević type functions

Abstract Using the more general method of differential subordinations founded by Miller and Mocanu (2000) [11] , several inclusion relations between certain classes consisting of α -convex type functions and Bazilevic type functions are first obtained, and their several interesting or important consequences along with some examples are then given.

STARLIKENESS AND CONVEXITY OF A CLASS OF ANALYTIC FUNCTIONS

Let be the class of analytic functions in the unit disk that are normalized with f(0)=f′(0)−1=0 and let −1≤BlA≤1. In this paper we study the class Gλ,α={f∈:|(1−α

Some applications of Hadamard convolution to multivalently analytic and multivalently meromorphic functions

The aim of the present study is to give several applications of Hadamard product (or convolution) to multivalently analytic and multivalently meromorphic functions.

A note involving p-valently Bazilević functions

A theorem involving p-valently Bazilevic functions is considered and then its certain consequences are given.

Certain operators and inequalities and their applications to meromorphically multivalent functions

In the present paper, making use of certain operators, some theorems involving inequalities on meromorphically multivalent functions in the punctured unit disk are obtained. Moreover, some of the results which are important for geometric function theory are also included.