ArticleOriginal scientific text
Title
On the class of functions strongly starlike of order α with respect to a point
Authors 1
Affiliations
- Department of Mathematics, Technical University of Rzeszów, W. Pola 2, 35-959 Rzeszów, Poland
Abstract
We consider the class (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 (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).
Keywords
functions starlike with respect to a point, starlike functions, strongly starlike functions, k-starlike functions, geometric characterization
Bibliography
- D. A. Brannan and W. E. Kirwan, On some classes of bounded univalent functions, J. London Math. Soc. (2) 1 (1969), 431-443.
- A. W. Goodman, Univalent Functions, Mariner, Tampa, Fla., 1983.
- W. Ma and D. Minda, An internal geometric characterization of strongly starlike functions, Ann. Univ. Mariae Curie-Skłodowska Sect. A 45 (1991), 89-97.
- J. Stankiewicz, On a family of starlike functions, Ann. Univ. Mariae Curie-Skłodowska Sect. A 22-24 (1968-70), 175-181.
- J. Stankiewicz, Quelques problèmes extrémaux dans les classes des fonctions α-angulairement étoilées, Ann. Univ. Mariae Curie-Skłodowska Sect. A 20 (1966), 59-75.
- J. K. Wald, On starlike functions, Ph.D. thesis, Univ. of Delaware, Newark, Del., 1978.