Disproof of a coefficient estimate related to Bazilevic functions

On Generalized Bazilevic Functions Related with Conic Regions

Let A denote the class of analytic functions f z defined in the unit disc E {z : |z| < 1} and satisfying the conditions f 0 0, f ′ 0 1. Let S denote the subclass of A consisting of univalent functions in E, and let S∗ and C be the subclasses of Swhich contains, respectively, star-like and convex in Bazilevič 1 introduced the class B α, β, h, g as follows. Let f ∈ A. Then, f ∈ B α, β, h, g , α, ...

On a New Subfamilies of Bazilevic Functions

In this paper, the author make use of the newly introduced concept of analytic functions by Kanas and Ronning [7] and apply Aouf et al derivative operator with the technique of Hayami, Owa and Srivastava [17] to define a more larger and generalized class of Bazilevic functions. Characterization and coefficient bounds of this new class of Bazilevic functions are considered. 2000 Mathematics Subj...

On a class of analytic functions related with generalized Bazilevic type functions

A lower estimate of harmonic functions

We shall give a lower estimate of harmonic‎ ‎functions of order greater than one in a half space‎, ‎which‎ ‎generalize the result obtained by B‎. ‎Ya‎. ‎Levin in a half plane‎.

Disproof of a Conjecture on Univalent Functions

We disprove the Gruenberg-RRnning-Ruscheweyh conjecture, namely that Re d g z (z) > 0; jzj < 1; holds for g 2 S, the set of normalized univalent functions in the unit disk D , and d analytic with jd 0 (z)j Re d(z) in D , d(0) = 1. Here stands for the Hadamard product.