In this paper, we consider some sufficient conditions for two integral operators to be starlike, close-to-convex and uniformly convex functions defined in the open unit disk. Mathematics subject classification (2000): 30C45.

The objective of the present paper is to give some characterizations for a (Gaussian) hypergeometric function to be in various subclasses of starlike and convex functions. We also consider an integral operator related to the hypergeometric function.

This paper deals with local convexity properties of the j-metric. We consider convexity and starlikeness of the j-metric balls in convex, starlike and general subdomains of R.

We introduce universally convex, starlike and prestarlike functions in the slit domain C \ [1,∞), and show that there exists a very close link to completely monotone sequences and Pick functions.

Inclusion relations for k−uniformly starlike functions under the Dziok-Srivastava operator are established. These results are also extended to k−uniformly convex functions, close-to-convex, and quasi-convex functions.

We prove the following new characterization of C (Lipschitz) smoothness in Banach spaces. An infinite-dimensional Banach space X has a C smooth (Lipschitz) bump function if and only if it has another C smooth (Lipschitz) bump function f such that its derivative does not vanish at any point in the interior of the support of f (that is, f does not satisfy Rolle’s theorem). Moreover, the support o...

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...

Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract Let U = {z ∈ C : |z| < 1} be the unit disc in the complex plane.Let Σ k be the class of meromorphic functions f in U having the form: f (z) = 1 z + α k z k + · · · , 0 < |z| < 1, k ≥ 0 A function f ∈ Σ = Σ 0 is called starlike...