Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2019.01.17
  • Accepted : 2019.08.26
  • Published : 2020.03.01
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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

Acknowledgement

The work presented here was supported by a Research Fellowship from the Department of Science and Technology, New Delhi.

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