On uniformly convex functions

A. W. Goodman

Annales Polonici Mathematici (1991)

  • Volume: 56, Issue: 1, page 87-92
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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A. W. Goodman. "On uniformly convex functions." Annales Polonici Mathematici 56.1 (1991): 87-92. <http://eudml.org/doc/262392>.

@article{A1991,
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.},
author = {A. W. Goodman},
journal = {Annales Polonici Mathematici},
keywords = {univalent functions; convex functions; coefficient bounds; circular arc; convex arc; uniformly convex functions},
language = {eng},
number = {1},
pages = {87-92},
title = {On uniformly convex functions},
url = {http://eudml.org/doc/262392},
volume = {56},
year = {1991},
}

TY - JOUR
AU - A. W. Goodman
TI - On uniformly convex functions
JO - Annales Polonici Mathematici
PY - 1991
VL - 56
IS - 1
SP - 87
EP - 92
AB - 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.
LA - eng
KW - univalent functions; convex functions; coefficient bounds; circular arc; convex arc; uniformly convex functions
UR - http://eudml.org/doc/262392
ER -

References

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  1. [1] A. W. Goodman, Univalent functions and nonanalytic curves, Proc. Amer. Math. Soc. 8 (1957), 598-601. Zbl0166.33002
  2. [2] A. W. Goodman, Univalent Functions, Polygonal Publ. Co. Inc., Washington, N.J., 1983. 
  3. [3] A. W. Goodman, On uniformly starlike functions, J. Math. Anal. Appl. 155 (1991), 364-370. Zbl0726.30013
  4. [4] W. Rudin, Function Theory in Polydiscs, Benjamin, New York 1969. 

Citations in EuDML Documents

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  1. Yong Chan Kim, Ern Gun Kwon, On some radius results for normalized analytic functions
  2. Wancang Ma, David Minda, Uniformly convex functions
  3. Wancang Ma, David Minda, Uniformly convex functions II
  4. G. Murugusundaramoorthy, Kaliappan Vijaya, Ravinder Krishna Raina, A subclass of harmonic functions with varying arguments defined by Dziok-Srivastava operator
  5. Firas Ghanim, Maslina Darus, On new subclass of analytic functions with respect to symmetric points
  6. G. Murugusundaramoorthy, K. Uma, Certain subclasses of starlike functions of complex order involving the Hurwitz-Lerch Zeta function
  7. Nihat Yagmur, Halit Orhan, Fekete-Szegő problem for subclasses of generalized uniformly starlike functions with respect to symmetric points
  8. R. M. El-Ashwah, M. K. Aouf, A. Shamandy, E. E. Ali, Subordination results for some subclasses of analytic functions

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