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

Annales Polonici Mathematici (1998)

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

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topAdam 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

top- [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] 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.

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