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http://dx.doi.org/10.4134/JKMS.j190051

APPLICATIONS OF DIFFERENTIAL SUBORDINATIONS TO CERTAIN CLASSES OF STARLIKE FUNCTIONS  

Banga, Shagun (Department of Applied Mathematics Delhi Technological University)
Kumar, S. Sivaprasad (Department of Applied Mathematics Delhi Technological University)
Publication Information
Journal of the Korean Mathematical Society / v.57, no.2, 2020 , pp. 331-357 More about this Journal
Abstract
Let p be an analytic function defined on the open unit disk 𝔻. We obtain certain differential subordination implications such as ψ(p) := pλ(z)(α+βp(z)+γ/p(z)+δzp'(z)/pj(z)) ≺ h(z) (j = 1, 2) implies p ≺ q, where h is given by ψ(q) and q belongs to 𝒫, by finding the conditions on α, β, γ, δ and λ. Further as an application of our derived results, we obtain sufficient conditions for normalized analytic function f to belong to various subclasses of starlike functions, or to satisfy |log(zf'(z)/f(z))| < 1, |(zf'(z)/f(z))2 - 1| < 1 and zf'(z)/f(z) lying in the parabolic region v2 < 2u - 1.
Keywords
$Carath{\acute{e}}odory$ function; differential subordinations; minimum principle; exponential function; strongly starlike function; lemniscate of Bernoulli; Janowski starlike function;
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