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arXiv · 2305.16210

Constrained Radius Estimates Of Certain Analytic Functions

Meghna Sharma·Naveen Kumar Jain·Sushil Kumar
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Abstract

Let $\mathcal{P}$ denote the Carath\'{e}odory class accommodating all the analytic functions $p$ having positive real part and satisfying $p(0)=1$. In this paper, the second coefficient of the normalized analytic function $f$ defined on the open unit disc is constrained to define new classes of analytic functions. The classes are characterised by the functions $f/g$ having positive real part or satisfying the inequality $|(f(z)/g(z))-1|<1$ such that $f(z)(1-z^2)/z$ and $g(z)(1-z^2)/z$ are Carath\'{e}odory functions for some analytic function $g$. This paper aims at determining radius of starlikeness for the introduced classes.

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Meghna Sharma, Naveen Kumar Jain, Sushil Kumar. 2023-05-25. Constrained Radius Estimates Of Certain Analytic Functions. https://arxiv.org/abs/2305.16210

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