Displaying similar documents to “Uniformly convex functions”

Univalent functions with logarithmic restrictions

A. Z. Grinshpan (1991)

Annales Polonici Mathematici

Similarity:

It is known that univalence property of regular functions is better understood in terms of some restrictions of logarithmic type. Such restrictions are connected with natural stratifications of the studied classes of univalent functions. The stratification of the basic class S of functions regular and univalent in the unit disk by the Grunsky operator norm as well as the more general one of the class 𝔐 * of pairs of univalent functions without common values by the τ-norm (this concept...

On uniformly convex functions

A. W. Goodman (1991)

Annales Polonici Mathematici

Similarity:

We introduce a new class of normalized functions regular and univalent in the unit disk. These functions, called uniformly convex functions, are defined by a purely geometric property. We obtain a few theorems about this new class and we point out a number of open problems.

Some Notes about a Class of Univalent Functions with Negative Coefficients

Pashkouleva, Donka (2010)

Fractional Calculus and Applied Analysis

Similarity:

MSC 2010: 30C45, 30C50 The object of this paper is to obtain sharp results involving coefficient bounds, growth and distortion properties for some classes of analytic and univalent functions with negative coefficients.

Integral representations of bounded starlike functions

Frode Rønning (1995)

Annales Polonici Mathematici

Similarity:

For α ≥ 0 let ℱ α denote the class of functions defined for |z| < 1 by integrating 1 / ( 1 - x z ) α if α > 0, and log(1/(1-xz)) if α = 0, against a complex measure on |x| = 1. We study families of starlike functions where zf’(z)/f(z) ranges over a parabola with given focus and vertex. We prove a number of properties of these functions, among others that they are bounded and that they belong to ℱ 0 . In general, it is only known that bounded starlike functions belong to ℱ α for α > 0.

Starlikeness of functions satisfying a differential inequality

Rosihan M. Ali, S. Ponnusamy, Vikramaditya Singh (1995)

Annales Polonici Mathematici

Similarity:

In a recent paper Fournier and Ruscheweyh established a theorem related to a certain functional. We extend their result differently, and then use it to obtain a precise upper bound on α so that for f analytic in |z| < 1, f(0) = f'(0) - 1 = 0 and satisfying Re{zf''(z)} > -λ, the function f is starlike.