Radius properties for analytic and p-valently starlike functions

Uyanik, Neslihan; Owa, Shigeyoshi

doi:10.1186/1029-242x-2011-107

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2018

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“…Subsequently, in [13], S * R -radii were obtained for various well-known classes of starlike functions. For more results on radius problems, see [7,12,16,38,39]. Motivated by all these works, in Section 2 , we consider the subordination inclusions, in which we compute the sharp bound on the parameter β so that a given differential subordination implication holds.…”

Section: Introductionmentioning

confidence: 99%

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Differential subordination and radius estimates for starlike functions associated with the Booth lemniscate

2018

Turk J Math

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Abstract:We obtain several inclusions between the class of functions with positive real part and the class of starlike univalent functions associated with the Booth lemniscate. These results are proved by applying the well-known theory of differential subordination developed by Miller and Mocanu and these inclusions give sufficient conditions for normalized analytic functions to belong to some subclasses of Ma-Minda starlike functions. In addition, by proving an associated technical lemma, we compute various radii constants such as the radius of starlikeness, radius of convexity, radius of starlikeness associated with the lemniscate of Bernoulli, and other radius estimates for functions in the class of functions associated with the Booth lemniscate. The results obtained are sharp.

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Section: Introductionmentioning

confidence: 99%

“…Subsequently, in [13], S * R -radii were obtained for various well-known classes of starlike functions. For more results on radius problems, see [7,12,16,38,39].…”

Section: Geometrically F ∈ Smentioning

confidence: 99%

Differential subordination and radius estimates for starlike functions associated with the Booth lemniscate

2018

Turk J Math

View full text Add to dashboard Cite

show abstract

Radius properties for analytic and p-valently starlike functions

Cited by 1 publication

References 2 publications

Differential subordination and radius estimates for starlike functions associated with the Booth lemniscate

Differential subordination and radius estimates for starlike functions associated with the Booth lemniscate

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