Close-to-convexity and Starlikeness of Analytic Functions

Lee, See Keong; Ravichandran, V.; Supramaniam, Shamani

doi:10.5556/j.tkjm.46.2015.1621

Cited by 2 publications

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References 16 publications

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“…For 0 ≤ β < 1, a function f ∈ A is said to be close-toconvex of order β [10,16] if Re(zf (z)/g(z)) > β for some g ∈ S * (in general, g need not be normalized but we add this extra normalization). More results regarding these classes can be found in [9,12]. Recently, the authors have investigated the sufficient conditions for a function to belong to various subclasses of starlike functions in [20,26,27].…”

Section: Introductionmentioning

confidence: 99%

Sufficient conditions for strong starlikeness

Sharma

Cho

Ravichandran

2020

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Let p be an analytic function defined on the open unit disc D with p(0) = 1 and 0 < α ≤ 1. The conditions on complex valued functions C, D and E are obtained for p to be subordinate to (Sufficient conditions for confluent (Kummer) hypergeometric function and generalized and normalized Bessel function of the first kind of complex order to be subordinate to ((1 + z)/(1 − z)) α are obtained as applications. The conditions on α and β are derived for p to be subordinate to ((1 + z)/(1 − z)) α when 1 + βzp (z)/p n (z) with n = 1, 2 is subordinate to 1 + 4z/3 + 2z 2 /3 =: ϕ CAR (z). Similar problems were investigated for Re p(z) > 0 when the functions p(z) + βzp (z)/p n (z) with n = 0, 2 is subordinate to ϕ CAR (z). The condition on β is determined for p to be subordinate to ((1 + z)/(1 − z)) α when p(z) + βzp (z)/p n (z) with n = 0, 1, 2 is subordinate to ((1 + z)/(1 − z)) α .

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