Sharma, K., Ravichandran, V. (2016). Applications of subordination theory to starlike functions. Bulletin of the Iranian Mathematical Society, 42(3), 761-777.

K. Sharma; V. Ravichandran. "Applications of subordination theory to starlike functions". Bulletin of the Iranian Mathematical Society, 42, 3, 2016, 761-777.

Sharma, K., Ravichandran, V. (2016). 'Applications of subordination theory to starlike functions', Bulletin of the Iranian Mathematical Society, 42(3), pp. 761-777.

Sharma, K., Ravichandran, V. Applications of subordination theory to starlike functions. Bulletin of the Iranian Mathematical Society, 2016; 42(3): 761-777.

Applications of subordination theory to starlike functions

^{1}Department of Mathematics, Atma Ram Sanatan Dharma College, University of Delhi, Delhi 110021, India.

^{2}Department of Mathematics, University of Delhi, Delhi--110007, India.

Receive Date: 13 February 2015,
Revise Date: 27 April 2015,
Accept Date: 27 April 2015

Abstract

Let $p$ be an analytic function defined on the open unit disc $\mathbb{D}$ with $p(0)=1.$ The conditions on $\alpha$ and $\beta$ are derived for $p(z)$ to be subordinate to $1+4z/3+2z^{2}/3=:\varphi_{C}(z)$ when $(1-\alpha)p(z)+\alpha p^{2}(z)+\beta zp'(z)/p(z)$ is subordinate to $e^{z}$. Similar problems were investigated for $p(z)$ to lie in a region bounded by lemniscate of Bernoulli $|w^{2}-1|=1$ when the functions $(1-\alpha)p(z)+\alpha p^{2}(z)+\beta zp'(z)$ , $(1-\alpha)p(z)+\alpha p^{2}(z)+\beta zp'(z)/p(z)$ or $p(z)+\beta zp'(z)/p^{2}(z)$ is subordinate to $\varphi_{C}(z)$. Related results for $p$ to be in the parabolic region bounded by the $RE w=|w-1|$ are investigated.

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