Startseite Mathematik Sharp bounds on the logarithmic coefficients of inverse functions for certain classes of univalent functions
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Sharp bounds on the logarithmic coefficients of inverse functions for certain classes of univalent functions

  • Sanju Mandal , Molla Basir Ahamed und Paweł Zaprawa EMAIL logo
Veröffentlicht/Copyright: 24. Oktober 2025
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Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 75 Heft 5

Abstract

This article aims to determine the sharp bounds for the logarithmic coefficients of inverse functions in several classes of univalent functions. We obtain the sharp bounds of logarithmic coefficients Γ1, Γ2 and Γ3 of the inverse functions for the classes of starlike and convex functions with respect to symmetric points respectively. In addition, we establish sharp inequalities for the second Hankel determinant H2,1Ff−1/2≤3/44 and H2,1Ff−1/2≤23/3264 of logarithmic coefficients of the inverse functions for starlike and convex functions associated with a lune region, where f−1 is the inverse function of f.

Keywords: Univalent functions; starlike functions; convex functions; Hankel Determinant; logarithmic coefficients; Schwarz functions
MSC 2010: Primary 30C45; Secondary 30C50

All authors actively worked on the research contained in the paper. All authors reviewed the manuscript.

Funding statement: The first named author is supported by CSIR-SRF (File No: 09/0096(12546)/2021-EMR-I, dated: 08/10/2024), Govt. of India, New Delhi. The second named author is supported by SERB, SUR/2022/002244, Govt. India.

Acknowledgement

The authors are grateful to the referees for their constructive suggestions and comments which have improved the quality of the paper.

  1. (Communicated by Marek Balcerzak)

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Received: 2024-11-18
Accepted: 2025-06-14
Published Online: 2025-10-24
Published in Print: 2025-10-27

© 2025 Mathematical Institute Slovak Academy of Sciences

Artikel in diesem Heft

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  3. Sums of Tribonacci numbers close to powers of 2
  4. Multiplicative functions k-additive on hexagonal numbers
  5. Monogenic even cyclic sextic polynomials
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https://doi.org/10.1515/ms-2025-0082
Schlagwörter für diesen Artikel
Univalent functions; starlike functions; convex functions; Hankel Determinant; logarithmic coefficients; Schwarz functions

Artikel in diesem Heft

  1. Copies of monomorphic structures
  2. Endomorphism kernel property for extraspecial and special groups
  3. Sums of Tribonacci numbers close to powers of 2
  4. Multiplicative functions k-additive on hexagonal numbers
  5. Monogenic even cyclic sextic polynomials
  6. Elegant proofs for properties of normalized remainders of Maclaurin power series expansion of exponential function
  7. Degree of independence in non-archimedean fields
  8. Remarks on some one-ended groups
  9. Some new characterizations of weights for hardy-type inequalities with kernels on time scales
  10. Inequalities for Riemann–Liouville fractional integrals in co-ordinated convex functions: A Newton-type approach
  11. Radius estimates for functions in the class 𝒰r(λ)
  12. Sharp bounds on the logarithmic coefficients of inverse functions for certain classes of univalent functions
  13. More q-congruences from Singh’s quadratic transformation
  14. Stability and controllability of cycled dynamical systems
  15. Existence, uniqueness, and multiplicity of radially symmetric k-admissible solutions for k-hessian equations
  16. Strong solution of a Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flows with surfactant
  17. Coincidence points via tri-simulation functions with an application in integral equations
  18. On Fong-Tsui conjecture and binormality of operators
  19. Riemannian maps of CR-submanifolds of Kaehler manifolds
  20. On structural numbers of topological spaces
  21. The κ-Fréchet-Urysohn property for Cp(X) is equivalent to baireness of B1(X)
  22. Weighted pseudo S-asymptotically (ω, c)-periodic solutions to fractional stochastic differential equations
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