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Coefficient bounds for convex functions associated with cosine function

  • Umar Raza , Mohsan Raza EMAIL logo and Paweł Zaprawa
Published/Copyright: June 9, 2025
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Abstract

In this paper, we study the class 𝒞cos of normalized analytic functions f satisfying 1 + z f''(z) / f'(z) ≺ cos(z). We obtain the sharp coefficient bounds and Hankel determinants of second and third order for functions for 𝒞cos. We also present the similar results for inverse and logarithm coefficients. These results improve the results recently obtained in [Marimuthu et al.: Coefficient estimates for starlike and convex functions associated with cosine function, Hacet. J. Math. Stat. 52 (2023), 596–618. Furthermore, our results provide examples of invariance of the coefficient bounds among the subclass of convex functions.

2020 Mathematics Subject Classification: Primary 30C45; 30C50

The work here is supported by HEC grant: 20-16367/NRPU/R&D/HEC/2021-2020.


  1. (Communicated by Stanisława Kanas)

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Received: 2024-07-20
Accepted: 2024-12-04
Published Online: 2025-06-09
Published in Print: 2025-06-26

© 2025 Mathematical Institute Slovak Academy of Sciences

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