# On uniformly convex functions

Annales Polonici Mathematici (1991)

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

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topA. 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

top- [1] A. W. Goodman, Univalent functions and nonanalytic curves, Proc. Amer. Math. Soc. 8 (1957), 598-601. Zbl0166.33002
- [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. Zbl0726.30013
- [4] W. Rudin, Function Theory in Polydiscs, Benjamin, New York 1969.

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- G. Murugusundaramoorthy, K. Uma, Certain subclasses of starlike functions of complex order involving the Hurwitz-Lerch Zeta function
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- R. M. El-Ashwah, M. K. Aouf, A. Shamandy, E. E. Ali, Subordination results for some subclasses of analytic functions

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