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arXiv · 1703.03590

First order differential subordination for functions with positive real part

O. P. Ahuja·Sushil Kumar·V. Ravichandran
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Abstract

Sharp estimates on $\beta$ are determined so that an analytic function $p$ defined on the open unit disk in the complex plane normalized by $p(0)=1$ is subordinate to some well known starlike functions with positive real part whenever $1+\beta z p'(z), \,\,1+\beta z p'(z)/p(z), \,\,\mbox{or}\,\,1+\beta z p'(z)/p^{2}(z)$ is subordinate to $\sqrt{1+z}$. Our results provide sharp version of previously known results.

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O. P. Ahuja, Sushil Kumar, V. Ravichandran. 2017-03-10. First order differential subordination for functions with positive real part. https://arxiv.org/abs/1703.03590

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