Integral transforms of functions with restricted derivatives

• Autorzy: Johnny E. Brown
• Języki publikacji: EN

Abstrakty

EN

We show that functions whose derivatives lie in a half-plane are preserved under the Pommerenke, Chandra-Singh, Libera, Alexander and Bernardi integral transforms. We determine precisely how these transforms act on such functions. We prove that if the derivative of a function lies in a convex region then the derivative of its Pommerenke, Chandra-Singh, Libera, Alexander and Bernardi transforms lie in a strictly smaller convex region which can be determined. We also consider iterates of these transforms. Best possible results are obtained.

Kategorie tematyczne

• 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
• 30C75: Extremal problems for conformal and quasiconformal mappings, other methods

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2007
• Tom: 91
• Numer: 1
• Strony: 85-97

Daty

wydano

2007

Twórcy

autor

Johnny E. Brown

• Department of Mathematics, Purdue University, West Lafayette, IN 47907, U.S.A.

Identyfikatory

DOI

10.4064/ap91-1-7