On q-Calculus and Starlike Functions

On Uniformly Starlike Functions

These are normalized functions regular and univalent in E: IzI < 1, for which f( E) is starlike with respect to the origin. Let y be a circle contained in E and let [ be the center of y. The Pinchuk question is this: Iff(z) is in ST, is it true thatf(y) is a closed curve that is starlike with respect tof(i)? In Section 5 we will see that the answer is no. There seems to be no reason to demand t...

On Janowski Starlike Functions

COEFFICIENT ESTIMATES OF NEW CLASSES OF q–STARLIKE AND q–CONVEX FUNCTIONS OF COMPLEX ORDER

We introduce new classes of q -starlike and q -convex functions of complex order involving the q -derivative operator defined in the open unit disc. Furthermore, we find estimates on the coefficients for second and third coefficients of these classes.

Certain subclass of $p$-valent meromorphic Bazilevi'{c} functions defined by fractional $q$-calculus operators

The aim of the present paper is to introduce and investigate a new subclass of Bazilevi'{c} functions in the punctured unit disk $mathcal{U}^*$ which have been described through using of the well-known fractional $q$-calculus operators, Hadamard product and a linear operator. In addition, we obtain some sufficient conditions for the func...

Some Results on Starlike and Convex Functions

Let A denotes the class of functions f(z) that are analytic in the unit disk U = {z : |z| < 1} and normalized by f(0) = f ′(0)− 1 = 0. Further, let f, g ∈ A. Then we say that f(z) is subordinate to g(z), and we write f(z) ≺ g(z), if there exists a function ω(z), analytic in the unit disk U , such that ω(0) = 0, |ω(z)| < 1 and f(z) = g(ω(z)) for all z ∈ U . Specially, if g(z) is univalent in U t...