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Starlike functions associated with exponential function and the lemniscate of Bernoulli

  • Kanika KhatterEmail author
  • V. Ravichandran
  • S. Sivaprasad Kumar
Original Paper
  • 217 Downloads

Abstract

Let f be the function defined on the open unit disk, with \(f(0)=0=f'(0)-1\), satisfying the subordinations \(zf'(z)/f(z)\prec \alpha + (1-\alpha )e^{z}\) or \(zf'(z)/f(z)\prec \alpha + (1-\alpha )\sqrt{1+ z}\) respectively, where \(0\le \alpha < 1\). The sharp radii has been determined for these functions to belong to several well-known classes. In addition, some inclusion relations and coefficient estimates are also obtained.

Keywords

Starlike functions Exponential function Lemniscate of Bernoulli Radius problems Coefficient estimate 

Mathematics Subject Classification

30C45 30C80 

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Copyright information

© Springer-Verlag Italia S.r.l. 2017

Authors and Affiliations

  • Kanika Khatter
    • 1
    Email author
  • V. Ravichandran
    • 2
  • S. Sivaprasad Kumar
    • 1
  1. 1.Department of Applied MathematicsDelhi Technological UniversityDelhiIndia
  2. 2.Department of MathematicsUniversity of DelhiDelhiIndia

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