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

Adam Lecko

Annales Polonici Mathematici (1998)

  • Volume: 68, Issue: 2, page 107-117
  • ISSN: 0066-2216

Abstract

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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).

How to cite

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Adam Lecko. "On the class of functions strongly starlike of order α with respect to a point." Annales Polonici Mathematici 68.2 (1998): 107-117. <http://eudml.org/doc/270146>.

@article{AdamLecko1998,
abstract = {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).},
author = {Adam Lecko},
journal = {Annales Polonici Mathematici},
keywords = {functions starlike with respect to a point; starlike functions; strongly starlike functions; k-starlike functions; geometric characterization; strongly starlike function; starlike with respect to a point},
language = {eng},
number = {2},
pages = {107-117},
title = {On the class of functions strongly starlike of order α with respect to a point},
url = {http://eudml.org/doc/270146},
volume = {68},
year = {1998},
}

TY - JOUR
AU - Adam Lecko
TI - On the class of functions strongly starlike of order α with respect to a point
JO - Annales Polonici Mathematici
PY - 1998
VL - 68
IS - 2
SP - 107
EP - 117
AB - 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).
LA - eng
KW - functions starlike with respect to a point; starlike functions; strongly starlike functions; k-starlike functions; geometric characterization; strongly starlike function; starlike with respect to a point
UR - http://eudml.org/doc/270146
ER -

References

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  1. [1] D. A. Brannan and W. E. Kirwan, On some classes of bounded univalent functions, J. London Math. Soc. (2) 1 (1969), 431-443. Zbl0177.33403
  2. [2] A. W. Goodman, Univalent Functions, Mariner, Tampa, Fla., 1983. 
  3. [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. [4] J. Stankiewicz, On a family of starlike functions, Ann. Univ. Mariae Curie-Skłodowska Sect. A 22-24 (1968-70), 175-181. 
  5. [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. [6] J. K. Wald, On starlike functions, Ph.D. thesis, Univ. of Delaware, Newark, Del., 1978. 

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