Starlikeness associated with lemniscate of Bernoulli

Vibha Madaan; Ajay Kumar; V. Ravichandran

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arXiv · 1806.05136

Starlikeness associated with lemniscate of Bernoulli

Vibha Madaan·Ajay Kumar·V. Ravichandran

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Abstract

For an analytic function $f$ on the unit disk $\mathbb{D}=\{z:|z|<1\}$ satisfying $f(0)=0=f'(0)-1,$ we obtain sufficient conditions so that $f$ satisfies $|(zf'(z)/f(z))^2-1|<1.$ The technique of differential subordination of first or second order is used. The admissibility conditions for lemniscate of Bernoulli are derived and employed in order to prove the main results.

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BibTeX RIS

Vibha Madaan, Ajay Kumar, V. Ravichandran. 2018-06-13. Starlikeness associated with lemniscate of Bernoulli. https://arxiv.org/abs/1806.05136

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