Linear invariance and integral operators of univalence functions

• Autorzy: Dorff M. , Szynal J.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we study a larger set than (1), namely the set of the minimal invariant family which contains (1), where / belongs to the linear invariant family, and thereby we obtain information about the univalence of (1). In particular, we determine the order of this minimal invariant family in the cases of univalent and convex univalent functions in D. As a result, we find the radius of close-to-convexity and the lower bound for the radius of univalence for the minimal invariant family in the case of convex univalent functions. This allows us to determine the exact region for (a, (3) where the corresponding minimal invariant family is univalent and close-to-convex. These results are sharp and generalize those which were obtained in [11].

Słowa kluczowe

EN

integral operators; convex functions; univalent functions

PL

funkcje univalentne; funkcje wypukłe; operatory integralne

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 1
• Strony: 47--57
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Dorff M.

• Department of Mathematics, Brigham Young University, Provo, UT 84602, USA

autor

Szynal J.

• Department of Applied Mathematics, Faculty of Economics, Maria Curie-Sklodowska University, 20-031 Lublin, Poland

Bibliografia

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