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arXiv · 2005.03714

Sufficient Conditions For Janowski Starlike Functions With Fixed Second Coefficient

Najla M. Alarifi
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Abstract

Let A,B,D,E belong to [-1, 1] and let p(z) be an analytic function with fixed initial coefficient defined in the open unit disk. Conditions on A,B,D,and E are determined so that 1+αzp'(z) being subordinated to (1+Dz)/(1+Ez) implies that p(z) is subordinated to (1+Az)/(1+Bz) and other similar implications involving 1+αzp'(z)/p(z), αp2(z)+λzp'(z),αp(z)+(1-α)p2(z)+λzp'(z),and (1-α)p(z)+{alpha}(1+zp'(z)/p(z)). Also, sufficient conditions for Janowski starlikeness with fixed second coefficient are obtained.

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Najla M. Alarifi. 2020-05-07. Sufficient Conditions For Janowski Starlike Functions With Fixed Second Coefficient. https://arxiv.org/abs/2005.03714

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