On Functions with Nonvanishing Divided Differences

✍ Scribed by Stephan Ruscheweyh

• Publisher: John Wiley and Sons
• Year: 1976
• Tongue: English
• Weight: 143 KB
• Volume: 73
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19760730110

✦ Synopsis

On Functions with Nonvanishing Divided Differences

By STEPHAN RUSCHEWEYH of Dortmund (Eingegangen am 1.11.1974)

where zit j = O , . . . , n, are distinct points in U. Obviously there exists a natural extension of this definition to the case of arbitrary points z j € U , j = O , . . . , n. We denote this extension also by [f(z); z0, . . . , z,] and call it the nth divided difference of f(z). Let A be the class of functions f(z) regular in U and normalized by f(0) = f ' ( O ) -1 =O. K is the class of functions fEA which map U univalently onto a convex domain.