10.30495/maca.2025.2049601.1119

A study on Fekete-Szegö inequality for a class of analytic functions satisfying subordinate conditions associated with Chebyshev polynomials

XML PDF
  • Muhammet Kamali*1,
  1. Department of Mathematics, Faculty of Sciences, Kyrgyz-Turkish Manas University, Chyngyz Aitmatov Avenue, Bishkek, Kyrgyz Republic

Published in Issue 2025-01-01

How to Cite

A study on Fekete-Szegö inequality for a class of analytic functions satisfying subordinate conditions associated with Chebyshev polynomials. (2025). Mathematical Analysis and Its Contemporary Applications, 7(1). https://doi.org/10.30495/maca.2025.2049601.1119

PDF views: 0

Abstract

We define a class of analytic functions, A(H, n, m, λ), satisfying the following condition Dn+m λ f(z) Dn λf(z) ≺H(z, t), where λ ≥0, n, m ∈N∗= N∪{0}, t ∈ 1 2, 1 and for all z ∈Ω. In this study, firstly give estimates for coefficients |a2| and |a3| of functions belong to this class. Furthermore, the Fekete- Szeg¨o inequality was examined for the functions belonging to this class.

Keywords

  • Analytic function,
  • Salagean Operator,
  • Coefficient estimates,
  • Fekete- Szeg¨o inequality
PDF

References

  1. S. Altınkaya and S. Yal¸cın, On the Chebyshev polynomial bounds for classes of univalent functions, Khayyam J. Math., 2(1) , (2016), 1–5.
  2. S. Altınkaya and S. Yal¸cın, On the Chebyshev coefficients for a general subclass of univalent functions, Turk. J. Math., 42 (2018), 2885–2890.
  3. F. M. AL-Oboudi, On univalent functions defined by a generalized Salagea operator, IJMMS, 27 (2004), 1429–1436.
  4. M. K. Aouf, H. E. Darwish, and A. A. Attiya, Generalization of certain subclasses of analytic functions with negative coefficients, Studia Univ. Babe¸s-Bolyai Math., 45(1) (2000), 11–22.
  5. M. C¸a˘glar, H. Orhan, and M. Kamali, Fekete-Szeg¨o Problem for a Subclass of Analytic Functions Associated with Chebyshev Polynomials, Bol. Soc. Parana. Mat., 40(3) (2022), 6 pp.
  6. H. E. Darwish, Certain subclasses of analytic functions with negative coefficients defined by generalised Salagean operator, Gen. Math., 15(4) (2007), 69–82.
  7. E. H. Doha, The first and second kind Chebyshev coefficients of the moments of the generalorder derivative of an infinitely differentiable function, Int. J. Comput. Math., 51 (1994), 21–35.
  8. J. Dziok, R. K. Raina, and J. Sokol, Application of Chebyshev polynomials to classes of analytic functions, Comptes Rendus L’Academia Sci. 353(5) (2015), 433–438.
  9. M. Fekete, and G. Szeg¨o, Eine Bemerkung ¨Uber ungerade schlichte Funktionen, J. London Math. Soc., 8 (1933), 85–89.
  10. J. C. Mason, Chebyshev polynomial approximations for the L-membrane eigenvalue problem, SIAM J. Appl. Math., 15 (1967), 172–186.
  11. N. Mustafa and E. Akbulut, Application of the second kind Chebyshev polynomial to the Fekete-Szeg¨o problem of certain class analytic functions, J. Sci. Engin. Res., 6(2) (2019), 154– 163.
  12. N. Mustafa and E. Akbulut, Application of the second kind Chebyshev polynomials to coefficient estimates of certain class analytic functions, Int. J. Appl. Sci. Math., 6 (2),(2019) 44-49.
  13. C. Ramachandran and K. Dhanalaksmi, Fekete-Szeg¨o inequality for the subclasses of analytic functions bounded by Chebyshev polynomial, Glob. J. Pure Appl. Math., 13(9) (2017), 4953– 4958.
  14. Gr. S¸t. Salagean, Subclasses of Univalent Functions, Lecture Notes in Mathematics, Springer- Verlag, Berlin, 1983.
  15. T. Sekine, Generalization of certain subclasses of analytic functions, Int. J. Math. Math. Sci. 10(4) (1987), 725–732.
  16. E. Szatmari and S¸. Altinkaya, Coefficient estimates and Fekete-Szeg¨o inequality for a class of analytic functions satisfying subordinate condition associated with Chebyshev polynomials, Acta Univ. Sapientiae, Math., 11(2) (2019), 430–436. KAMALI
  17. E. T. Whittaker and G. N. Watson, A course on Modern Analysis, An introduction to the general theory of infinite process of analytic functions with an account of the principal transcendental functions, Fourth Edition, Cambridge University Press, 1963.