ArticleOriginal scientific text

Title

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

Authors 1

Affiliations

  1. 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

  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.
Pages:
107-117
Main language of publication
English
Received
1996-03-04
Accepted
1997-06-12
Published
1998
Exact and natural sciences