Have a personal or library account? Click to login
Upper bound of second Hankel determinant for bi-univalent functions with respect to symmetric conjugate Cover

Upper bound of second Hankel determinant for bi-univalent functions with respect to symmetric conjugate

Open Access
|Dec 2020

References

  1. [1] R. M. Ali, S. K. Lee, V. Ravichandran, S. Supramaniam, The Fekete-Szegö coefficient functional for transforms of analytic functions, Bull. Iranian Math. Soc., vol. 35, 2009, 119-142.
  2. [2] S. Altinkaya S. Yalçin, Fekete-Szegö inequalities for classes of bi-univalent functions defined by subordination, Adv. Math. Sci. J., vol. 3, 2014, 63-71.
  3. [3] S. Altinkaya, S. Yalçin, Coefficient estimates for two new subclasses of biunivalent functions with respect to symmetric points, J. Funct. Spaces, Art. ID 145242, 2015, 1-5.10.1155/2015/145242
  4. [4] S. Altinkaya, S. Yalçin, Second Hankel determinant for a general subclass of bi-univalent functions, TWMS J. Pure Appl. Math., vol. 7, no. 1, 2016, 98-104.
  5. [5] M. Caglar, H. Orhan, N. Yagmur, Coefficient bounds for new subclasses of biunivalent functions, Filomat, vol. 27, 2013, 1165-1171.10.2298/FIL1307165C
  6. [6] D. G. Cantor, Power series with integral Coefficients, Bull. Amer. Math. Soc., vol. 69, 1963, 362-366.10.1090/S0002-9904-1963-10923-4
  7. [7] V. K. Deekonda, R. Thoutreedy, An upper bound to the second Hankel determinant for functions in Mocanu class, Vietnam J. Math., vol. 43, 2015, 541-549.10.1007/s10013-014-0094-y
  8. [8] E. Deniz, M. Caglar, H. Orhan, Second Hankel determinant for bi-starlike and bi-convex functions of order β, Appl. Math. Comput., vol. 271, 2015, 301-307.10.1016/j.amc.2015.09.010
  9. [9] P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Band 259, Springer Verlag, New York, Berlin, Heidelberg and Tokyo, 1983.
  10. [10] R. M. El-Ashwah, D. K. Thomas, Some subclasses of close-to-convex functions, J. Ramanujan Math. Soc., vol. 2, 1987, 86-100.
  11. [11] M. Fekete, G. Szegö, Eine Bemerkung Uber Ungerade Schlichte Funktionen, J. Lond. Math. Soc., vol. 2, 1933, 85-89.10.1112/jlms/s1-8.2.85
  12. [12] U. Grenander, G. Szegö, Toeplitz Forms and Their Applications, California Monographs in Mathematical Sciences Univ. California Press, Berkeley, 1958.
  13. [13] A. Janteng, S. A. Halim, M. Darus, Hankel determinant for starlike and convex functions, Int. J. Math. Anal., vol. 1, no. 13, 2007, 619-625.
  14. [14] S. K. Lee, V. Ravichandran, S. Supramaniam, Bounds for the second Hankel determinant of certain univalent functions, J. Ineq. Appl., vol. 281, 2013, 1-17.10.1186/1029-242X-2013-281
  15. [15] A. K. Mishra, S. N. Kund, The second Hankel determinant for a class of analytic functions associated with the Carlson-Shaffer operator, Tamkang J. Math., vol. 44, 2013, 73-82.10.5556/j.tkjm.44.2013.963
  16. [16] J. W. Noonan, D. K. Thomas, On the second Hankel determinant of a really mean p-valent functions, Trans. Amer. Math. Soc., vol. 223, no. 2, 1976, 337-346.10.1090/S0002-9947-1976-0422607-9
  17. [17] H. Orhan, N. Magesh V. K. Balaji, Initial Coefficient bounds for a general class of bi-univalent functions, Filomat, vol. 29, 2015, 1259-1267.10.2298/FIL1506259O
  18. [18] Ch. Pommerenke, Univalent Functions, Vandenhoeck and Rupercht, Göttingen, 1975.
  19. [19] H. M. Srivastava, S. S. Eker, S. G. Hamidi, J. M. Jahangiri, Faber polynomial Coefficient estimates for bi-univalent functions defined by the Tremblay fractional derivative operator, Bull. Iranian Math. Soc., vol. 44, no. 1, 2018, 149-157.10.1007/s41980-018-0011-3
  20. [20] H. M. Srivastava, S. Gaboury, F. Ghanim, Coefficient estimates for some general subclasses of analytic and bi-univalent functions, Afr. Mat., vol. 28, 2017, 693-706.10.1007/s13370-016-0478-0
  21. [21] H. M. Srivastava, A. K. Mishra, P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., vol. 23, 2010, 1188-1192.10.1016/j.aml.2010.05.009
  22. [22] H. M. Srivastava, A. K. Wanas, Initial Maclaurin Coefficient bounds for new subclasses of analytic and m-fold symmetric bi-univalent functions defined by a linear combination, Kyungpook Math. J., vol. 59, no. 3, 2019, 493-503.
  23. [23] A. K. Wanas, Bounds for initial Maclaurin Coefficients for a new subclasses of analytic and m-Fold symmetric bi-univalent functions, TWMS J. App. Eng. Math., vol. 10, no. 2, 2020, 305-311.
  24. [24] A. K. Wanas, Applications of Chebyshev polynomials on λ-pseudo bi-starlike and λ-pseudo bi-convex functions with respect to symmetrical points, TWMS J. App. Eng. Math., vol. 10, no. 3, 2020, 568-573.
  25. [25] A. K. Wanas, A. L. Alina, Applications of Horadam polynomials on Bazilevič bi-univalent function satisfying subordinate conditions, Journal of Physics: Conf. Series, vol. 1294, 2019, 1-6.
  26. [26] A. K. Wanas, S. Yalçin, Initial Coefficient estimates for a new subclasses of analytic and m-Fold symmetric bi-univalent functions, Malaya Journal of Matematik, vol. 7, no. 3, 2019, 472-476.10.26637/MJM0703/0018
  27. [27] P. Zaprawa, On the Fekete-Szegö problem for classes of bi-univalent functions, Bull. Belg. Math. Soc. Simon Stevin, vol. 21, 2014, 169-178.10.36045/bbms/1394544302
  28. [28] P. Zaprawa, Estimates of initial Coefficients for bi-univalent functions, Abstr. Appl. Anal., Art. ID 357480, 2014, 1-6.10.1155/2014/357480
DOI: https://doi.org/10.2478/gm-2020-0016 | Journal eISSN: 1584-3289 | Journal ISSN: 1221-5023
Language: English
Page range: 67 - 80
Submitted on: Aug 14, 2020
|
Accepted on: Oct 18, 2020
|
Published on: Dec 31, 2020
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2020 Abbas Kareem Wanas, Serap Bulut, published by Lucian Blaga University of Sibiu
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.