On uniformly convex functions

• Autorzy: A. W. Goodman
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

univalent functions; convex functions; coefficient bounds

Kategorie tematyczne

• 30C50: Coefficient problems for univalent and multivalent functions
• 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1991-1992
• Tom: 56
• Numer: 1
• Strony: 87-92

Daty

wydano

1991

otrzymano

1990-09-01

Twórcy

autor

A. W. Goodman

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

Bibliografia

• [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.