2015
DOI: 10.1515/ms-2015-0093
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On Booth Lemniscate and Hadamard Product of Analytic Functions

Abstract: In [RUSCHEWEYH, S.-SHEIL-SMALL, T.: Hadamard product of schlicht functions and the Poyla-Schoenberg conjecture, Comment. Math. Helv. 48 (1973), 119-135] the authors proved the P`olya-Schoenberg conjecture that the class of convex univalent functions is preserved under convolution, namely K ∗ K = K. They proved also that the class of starlike functions and the class of close-to-convex functions are closed under convolution with the class K. In this paper we consider similar convolution problems for some classes… Show more

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Cited by 10 publications
(4 citation statements)
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“…The function F q (z) was studied in [27,28]. The function F q (z) is a starlike univalent when q 2 < 1.…”
Section: Remark 11mentioning
confidence: 99%
“…The function F q (z) was studied in [27,28]. The function F q (z) is a starlike univalent when q 2 < 1.…”
Section: Remark 11mentioning
confidence: 99%
“…where G is the family of function univalent, convex in one direction, and satisfying {1 + zf (z)/f (z)} > −1/2, see [12]. [8]. Summarizing, T α,β,γ is a analytic univalent function with positive real part in D, T α,β,γ (D) is symmetric with respect to the real axis, starlike with respect to T α,β,γ (0) = 1 and convex in one direction under some conditions on α and β.…”
Section: Subclass Of the Carathèodory Class Related To The Generalize...mentioning
confidence: 99%
“…In 2015, Piejko and Sokó l [24] proved that the function z/(1 − αz 2 ) is convex univalent for 0 ≤ α < 3 − 2 √ 2 and also discussed some convolution properties related to the functions in the class BS * (α). Using the representation formula, we see that the function…”
Section: Radius Estimatesmentioning
confidence: 99%
“…In [11], various radius problems and subordination results were also discussed for some subclasses of analytic functions. For more details, see [24]. The Booth lemniscate is a special case of the Persian curve [29] and it was named after Booth, an Irish mathematician, who studied it in 1873.…”
Section: Introductionmentioning
confidence: 99%