Have a personal or library account? Click to login
Coefficient bounds for q-convex functions related to q-Bernoulli numbers Cover
Open Access
|Apr 2025

References

  1. O. P. Ahuja, A. etinkaya and Y. Polatoğlu, Bieberbach-de Branges and Fekete-Szeg inequalities for certain families of q-convex and q-close-to-convex functions, J. Comput. Anal. Appl. 26(4) (2019), 639–649 .
  2. H. Aldweby, M. Darus, Coefficient estimates of classes of q-starlike and q-convex functions, Advanced Studies in Contemporary Mathematics, 26 (1) (2016), 21-26.
  3. W. A. Al-Salam, q-Bernoulli numbers and polynomials, Math. Nachr. Vol. 17 (1959), 239-260.
  4. D. G. Cantor, Power series with integral coefficients, Bull. Amer. Math. Soc. 69 (1963), 362–366.
  5. L. Carlitz, q-Bernoulli numbers and polynomials, Duke Math. J. 15 (1948), 987–1000.
  6. J. Choi, P. J. Anderson and H. M. Srivastava, Carlitz’s q-Bernoulli and q-Euler numbers and polynomials and a class of q-Hurwitz zeta functions, Appl. Math. Comput. 215 (2009), 1185-1208.
  7. M. ağlar, H. Orhan, H. M. Srivastava, Coefficient bounds for q-starlike functions associated with q-Bernoulli numbers, Journal of Applied Analysis and Computation, 13(4) (2023), 2354-2364.
  8. U. Grenander, G. Szeg, Toeplitz forms and their applications, California Monographs in Mathematical Sciences Univ. California Press, Berkeley, 1958.
  9. M. E. H. Ismail, E. Merkes, D. Styer, A generalization of starlike functions, Complex Var. Theory Appl. 14 (1990), 77–84.
  10. F. H. Jackson, On q-definite integrals, Quarterly J. Pure Appl. Math., 41 (1910), 193–203.
  11. F. H. Jackson, On q-functions and a certain difference operator, Transactions of the Royal Society of Edinburgh, 46 (1908), 253–281.
  12. V. Kac and P. Cheung, Quantum Calculus, Springer, New York, 2002.
  13. N. Koblitz, On Carlitz’s q-Bernoulli numbers, J. Number Theory 14 (1982), 332–339.
  14. S. Mahmood, Q. Z. Ahmad, H. M. Srivastava, N. Khan, B. Khan, M. Tahir, A certain subclass of meromorphically q-starlike functions associated with the Janowski functions, J. Inequal. Appl. 2019 (2019), 88.
  15. S. Mahmood, M. Jabeen, S. N. Malik, H. M. Srivastava, R. Manzoor, S. M. J. Riaz, Some coefficient inequalities of q-starlike functions associated with conic domain defined by q-derivative, J. Funct. Spaces 2018 (2018), 8492072.
  16. S. Mahmood, H. M. Srivastava, N. Khan, Q. Z. Ahmad, B. Khan, I. Ali, Upper bound of the third Hankel determinant for a subclass of q-starlike functions, Symmetry 11 (2019), 347.
  17. S. Nalci, O. K. Pashaev, q-Bernoulli numbers and zeros of q-Sine function, arxiv:1202.2265v1, 2012.
  18. J. W. Noonan, D. K. Thomas, On the second Hankel determinant of areally mean p-valent functions, Trans. Amer. Math. Soc., 223 (2) (1976), 337-346.
  19. Y. Polatoğlu, Growth and distortion theorems for generalized q-starlike functions, Advances in Mathematics Scientific Journal 5 (1) (2016), 7-12.
  20. Ch. Pommerenke, Univalent Functions, Vandenhoeck and Rupercht, Gvttingen, 1975.
  21. C. S. Ryoo, A note on q-Bernoulli numbers and p olynomials, Appl. Math. Lett. Vol. 20 (2007), 524-531.
  22. T. M. Seoudy, M. K. Aouf, Coefficent estimates of new classes q-starlike and q-convex functions of complex order, Journal of Mathematical Inequalities Volume 10, Number 1 (2016), 135–145.
  23. H. M. Srivastava, Univalent Functions, Fractional Calculus, and Associated Generalized Hypergeometric Functions, in: H. M. Srivastava, S. Owa (Eds.), Univalent Functions, Fractional Calculus, and Their Applications, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1989, 329–354.
  24. H. M. Srivastava, Some formulas for the Bernoulli and Euler polynomials at rational arguments, Math. Proc. Cambridge Philos. Soc. 129 (2000), 77-84.
  25. H. M. Srivastava, Some generalizations and basic (or q-) extensions of the Bernoulli, Euler and Genocchi polynomials, Appl. Math. Inform. Sci. 5 (2011), 390-444.
  26. H. M. Srivastava, M. Tahir, B. Khan, Q. Z. Ahmad, N. Khan, Some general classes of q-starlike functions associated with the Janowski functions, Symmetry 11 (2019), 292.
  27. H. M. Srivastava, M. Tahir, B. Khan, Q. Z. Ahmad, N. Khan, Some general families of q-starlike functions associated with the Janowski functions, Filomat 33 (2019), 2613–2626.
  28. H. M. Srivastava, B. Khan, N. Khan, Q. Z. Ahmad, Coefficient inequalities for q-starlike functions associated with the Janowski functions, Hokkaido Math. J. 48 (2019), 407–425.
  29. H. M. Srivastava, Q. Z. Ahmad, N. Khan, N. Khan, B. Khan, Hankel and Toeplitz determinants for a subclass of q-starlike functions associated with a general conic domain, Mathematics 7 (2) (2019), 181.
  30. H. M. Srivastava, B. Khan, N. Khan, M. Tahir, S. Ahmad, N. Khan, Upper bound for a subclass of q-starlike functions associated with the q-exponential function, Bull. Sci. Math. 167 (2021), 102942.
  31. A. Soni, A. etinkaya, Fekete-Szeg inequalities for q-starlike and q-convex functions involvıng q-analogue of Ruscheweyh-type differential operator. Palestine Journal of Mathematics, 11(1) (2022), 541–548.
  32. H. E. . Uar, Coefficient inequality for q-starlike functions, Appl. Math. Comput. 276 (2016), 122-126.
  33. B. Wongsaijai, N. Sukantamala, Certain properties of some families of generalized starlike functions with respect to q-calculus, Abstr. Appl. Anal. 2016 (2016), 6180140.
DOI: https://doi.org/10.2478/auom-2025-0005 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784
Language: English
Page range: 77 - 92
Submitted on: Jan 7, 2024
Accepted on: Apr 30, 2024
Published on: Apr 2, 2025
Published by: Ovidius University of Constanta
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2025 Daniel Breaz, Halit Orhan, Hava Arıkan, Luminiţa-Ioana Cotîrlă, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.