Generalized problem of starlikeness for products of close-to-star functions

• Autorzy: Jacek Dziok
• Języki publikacji: EN

Abstrakty

EN

We consider functions of the type $F(z) = z∏_{j=1}^{n}[f_{j}(z)/z]^{a_{j}}$, where $a_{j}$ are real numbers and $f_{j}$ are $β_{j}$-strongly close-to-starlike functions of order ${α_{j}}$. We look for conditions on the center and radius of the disk 𝓓(a,r) = {z:|z-a| < r}, |a| < r ≤ 1 - |a|, ensuring that F(𝓓(a,r)) is a domain starlike with respect to the origin.

Kategorie tematyczne

• 30C50: Coefficient problems for univalent and multivalent functions
• 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
• 30C55: General theory of univalent and multivalent functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2013
• Tom: 107
• Numer: 2
• Strony: 109-121

Daty

wydano

2013

Twórcy

autor

Jacek Dziok

• Institute of Mathematics, University of Rzeszów, 35-310 Rzeszów, Poland

Identyfikatory

DOI

10.4064/ap107-2-1