On the class of functions strongly starlike of order α with respect to a point

• Autorzy: Adam Lecko
• Języki publikacji: EN

Abstrakty

EN

We consider the class 𝓩(k;w), k ∈ [0,2], w ∈ ℂ, of plane domains Ω called k-starlike with respect to the point w. An analytic characterization of regular and univalent functions f such that f(U) is in 𝓩(k;w), where w ∈ f(U), is presented. In particular, for k = 0 we obtain the well known analytic condition for a function f to be starlike w.r.t. w, i.e. to be regular and univalent in U and have f(U) starlike w.r.t. w ∈ f(U).

Słowa kluczowe

EN

functions starlike with respect to a point   starlike functions   strongly starlike functions   k-starlike functions   geometric characterization  

Kategorie tematyczne

• 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: 1998
• Tom: 68
• Numer: 2
• Strony: 107-117

Daty

wydano

1998

otrzymano

1996-03-04

poprawiono

1997-06-12

poprawiono

1997-10-20

Twórcy

autor

Adam Lecko

• Department of Mathematics, Technical University of Rzeszów, W. Pola 2, 35-959 Rzeszów, Poland

Bibliografia

• [1] D. A. Brannan and W. E. Kirwan, On some classes of bounded univalent functions, J. London Math. Soc. (2) 1 (1969), 431-443.
• [2] A. W. Goodman, Univalent Functions, Mariner, Tampa, Fla., 1983.
• [3] W. Ma and D. Minda, An internal geometric characterization of strongly starlike functions, Ann. Univ. Mariae Curie-Skłodowska Sect. A 45 (1991), 89-97.
• [4] J. Stankiewicz, On a family of starlike functions, Ann. Univ. Mariae Curie-Skłodowska Sect. A 22-24 (1968-70), 175-181.
• [5] J. Stankiewicz, Quelques problèmes extrémaux dans les classes des fonctions α-angulairement étoilées, Ann. Univ. Mariae Curie-Skłodowska Sect. A 20 (1966), 59-75.
• [6] J. K. Wald, On starlike functions, Ph.D. thesis, Univ. of Delaware, Newark, Del., 1978.