Download PDF - On uniformly convex functionsAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

On uniformly convex functions

Authors 1

Affiliations

  1. Department of Mathematics, University of South Florida, Tampa, Florida 33620-5700, U.S.A.

Abstract

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.

Keywords

ENG
univalent functions, convex functions, coefficient bounds

Bibliography

  1. A. W. Goodman, Univalent functions and nonanalytic curves, Proc. Amer. Math. Soc. 8 (1957), 598-601.
  2. A. W. Goodman, Univalent Functions, Polygonal Publ. Co. Inc., Washington, N.J., 1983.
  3. A. W. Goodman, On uniformly starlike functions, J. Math. Anal. Appl. 155 (1991), 364-370.
  4. W. Rudin, Function Theory in Polydiscs, Benjamin, New York 1969.
Annales Polonici Mathematici
1991-1992/56/1
Export to PBN, Opens in new tab
Pages:
87-92
Main language of publication
English
Received
1990-09-01
Published
1991
Exact and natural sciences