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Radius problem associated with certain ratios and linear combinations of analytic functions

  • Priya G. Krishnan EMAIL logo , Ravichandran Vaithiyanathan and Ponnaiah Saikrishnan
Published/Copyright: August 14, 2024
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Abstract

For normalized starlike functions f : 𝔻 → ℂ, we consider the analytic functions g : 𝔻 → ℂ defined by g(z) = (1 + z(f″(z))/f′(z))/(zf′(z)/f(z)) and g(z) = (1 − α)(zf′(z))/f(z) + α(1 + (zf″(z))/f′(z)), 0 ≤ α ≤ 1. We determine the largest radius ρ with 0 < ρ ≤ 1 such that g(ρ z) is subordinate to various functions with positive real part.

MSC 2010: 30C80; 30C45

The first author is supported by Senior Research Fellowship from University Grants Commission, New Delhi


  1. Communicated by Stanisława Kanas

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Received: 2023-09-02
Accepted: 2023-12-05
Published Online: 2024-08-14
Published in Print: 2024-08-27

© 2024 Mathematical Institute Slovak Academy of Sciences

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