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Close-to-convex functions associated with a rational function

  • Swati Anand , Pratima Rai and Sushil Kumar EMAIL logo
Published/Copyright: May 24, 2024
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Abstract

In this paper, we consider the class 𝓚𝓢(ψ0) of close-to-convex functions associated to a rational function ψ0(z) = (k2 + z2)/(k2kz), where k = 2 + 1 and the rational function ψ0 is related to cardioid shaped bounded domain. We compute the radius of convexity, growth, distortion and certain coefficient inequalities of such functions. We determine bounds on second and third order Toeplitz determinants. Moreover, we also compute bounds on second order Hankel determinants and second and third order Vandermonde determinants.

MSC 2010: 30C45

This work was supported by the Institute of Eminence, University of Delhi, Delhi, India–110007, Grant No. /IoE/2021/12/FRP


Acknowledgement

The authors are thankful to the referee for his valuable comments.

  1. Communicated by Stanisława Kanas

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Received: 2023-03-21
Accepted: 2023-08-24
Published Online: 2024-05-24
Published in Print: 2024-04-25

© 2024 Mathematical Institute Slovak Academy of Sciences

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