Upper bound to second Hankel determinant for a family of bi-univalent functions
DOI:
https://doi.org/10.5269/bspm.51332Resumen
In the current investigation, we study a certain family of analytic and bi-univalent functions with respect to symmetric conjugate points defined in the open unit disk $U$ and find an upper bounds for the second Hankel determinant $H_{2}(2)$ of the functions belongs to this class.Referencias
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2. Ali, R. M., Lee, S. K., Ravichandran, V. and Supramaniam, S., Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions, Appl. Math. Lett. 25, 344-351, (2012).
3. Altınkaya, S. and Yalcin, S., Fekete-Szego inequalities for classes of bi-univalent functions defined by subordination, Adv. Math. Sci. J. 3, 63-71, (2014).
4. Altınkaya, S. and Yalcin, S., Initial coefficient bounds for a general class of bi-univalent functions, Int. J. Anal. 2014, Art. ID 867871, 1-4, (2014).
5. Altınkaya, S. and Yalcin, S., Coefficient estimates for two new subclasses of bi-univalent functions with respect to symmetric points, J. Funct. Spaces 2015, Art. ID 145242, 1-5, (2015).
6. S. Altınkaya, S¸. and Yalcin, S., Second Hankel determinant for a general subclass of bi-univalent functions, TWMS J. Pure Appl. Math. 7, no. 1, 98-104, (2016).
7. Caglar, M., Orhan, H. and Yagmur, N., Coefficient bounds for new subclasses of bi-univalent functions, Filomat 27, 1165-1171, (2013).
8. Cantor, D. G., Power series with integral coefficients, Bull. Amer. Math. Soc. 69, 362-366, (1963)
9. Deekonda, V. K. and Thoutreedy, R., An upper bound to the second Hankel determinant for functions in Mocanu class, Vietnam J. Math. 43, 541-549, (2015).
10. Deniz, E., Caglar, M. and Orhan, H., Second Hankel determinant for bi-starlike and bi-convex functions of order β, Appl. Math. Comput. 271, 301-307, (2015).
11. Duren, P. L., Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Band 259, Springer Verlag, New York, Berlin, Heidelberg and Tokyo, (1983).
12. El-Ashwah, R. M. and Thomas, D. K., Some subclasses of close-to-convex functions, J. Ramanujan Math. Soc. 2, 86-100, (1987).
13. Fekete, M. and Szego, G., Eine Bemerkung Uber Ungerade Schlichte Funktionen, J. Lond. Math. Soc. 2, 85-89, (1933).
14. Frasin, B. A. and Aouf, M. K., New subclasses of bi-univalent functions, Appl. Math. Lett. 24, 1569-1573, (2011).
15. Grenander, U. and Szego, G., Toeplitz Forms and Their Applications, California Monographs in Mathematical Sciences Univ. California Press, Berkeley, (1958).
16. Janteng, A. S., Halim, A. and Darus, M., Hankel determinant for starlike and convex functions, Int. J. Math. Anal. 1, no. 13, 619-625, (2007).
17. Lee, S. K., Ravichandran, V. and Supramaniam, S., Bounds for the second Hankel determinant of certain univalent functions, J. Ineq. Appl. 281, 1-17, (2013).
18. Mishra, A. K. and Kund, S. N., The second Hankel determinant for a class of analytic functions associated with the Carlson-Shaffer operator, Tamkang J. Math. 44, 73-82, (2013).
19. Noonan, J. W. and Thomas, D. K., On the second Hankel determinant of a really mean p-valent functions, Trans. Amer. Math. Soc. 223, no. 2, 337-346, (1976).
20. Orhan, H., Magesh, N. and Balaji, V. K., Initial coefficient bounds for a general class of bi-univalent functions, Filomat 29, 1259-1267, (2015).
21. Pommerenke, Ch., Univalent Functions, Vandenhoeck and Rupercht, G¨ottingen, (1975).
22. Srivastava, H. M., Eker, S. S., Hamidi, S. G. and Jahangiri, J. M., Faber polynomial coefficient estimates for bi-univalent functions defined by the Tremblay fractional derivative operator, Bull. Iranian Math. Soc. 44, no. 1, 149-157, (2018).
23. Srivastava, H. M., Mishra, A. K. and Gochhayat, P., Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23, 1188-1192, (2010).
24. Wanas, A. K. and Majeed, A. H., Chebyshev polynomial bounded for analytic and bi-univalent functions with respect to symmetric conjugate points, Applied Mathematics E-Notes 19, 14-21, (2019).
25. Wanas, A. K. and Alina, A. L., Applications of Horadam polynomials on Bazileviˇc bi-univalent function satisfying subordinate conditions, Journal of Physics: Conf. Series 1294, 1-6, (2019).
26. Zaprawa, P., On the Fekete-Szego problem for classes of bi-univalent functions, Bull. Belg. Math. Soc. Simon Stevin 21, 169-178,(2014).
27. Zaprawa, P., Estimates of initial coefficients for bi-univalent functions, Abstr. Appl. Anal. 2014, Art. ID 357480, 1-6, (2014).
2. Ali, R. M., Lee, S. K., Ravichandran, V. and Supramaniam, S., Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions, Appl. Math. Lett. 25, 344-351, (2012).
3. Altınkaya, S. and Yalcin, S., Fekete-Szego inequalities for classes of bi-univalent functions defined by subordination, Adv. Math. Sci. J. 3, 63-71, (2014).
4. Altınkaya, S. and Yalcin, S., Initial coefficient bounds for a general class of bi-univalent functions, Int. J. Anal. 2014, Art. ID 867871, 1-4, (2014).
5. Altınkaya, S. and Yalcin, S., Coefficient estimates for two new subclasses of bi-univalent functions with respect to symmetric points, J. Funct. Spaces 2015, Art. ID 145242, 1-5, (2015).
6. S. Altınkaya, S¸. and Yalcin, S., Second Hankel determinant for a general subclass of bi-univalent functions, TWMS J. Pure Appl. Math. 7, no. 1, 98-104, (2016).
7. Caglar, M., Orhan, H. and Yagmur, N., Coefficient bounds for new subclasses of bi-univalent functions, Filomat 27, 1165-1171, (2013).
8. Cantor, D. G., Power series with integral coefficients, Bull. Amer. Math. Soc. 69, 362-366, (1963)
9. Deekonda, V. K. and Thoutreedy, R., An upper bound to the second Hankel determinant for functions in Mocanu class, Vietnam J. Math. 43, 541-549, (2015).
10. Deniz, E., Caglar, M. and Orhan, H., Second Hankel determinant for bi-starlike and bi-convex functions of order β, Appl. Math. Comput. 271, 301-307, (2015).
11. Duren, P. L., Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Band 259, Springer Verlag, New York, Berlin, Heidelberg and Tokyo, (1983).
12. El-Ashwah, R. M. and Thomas, D. K., Some subclasses of close-to-convex functions, J. Ramanujan Math. Soc. 2, 86-100, (1987).
13. Fekete, M. and Szego, G., Eine Bemerkung Uber Ungerade Schlichte Funktionen, J. Lond. Math. Soc. 2, 85-89, (1933).
14. Frasin, B. A. and Aouf, M. K., New subclasses of bi-univalent functions, Appl. Math. Lett. 24, 1569-1573, (2011).
15. Grenander, U. and Szego, G., Toeplitz Forms and Their Applications, California Monographs in Mathematical Sciences Univ. California Press, Berkeley, (1958).
16. Janteng, A. S., Halim, A. and Darus, M., Hankel determinant for starlike and convex functions, Int. J. Math. Anal. 1, no. 13, 619-625, (2007).
17. Lee, S. K., Ravichandran, V. and Supramaniam, S., Bounds for the second Hankel determinant of certain univalent functions, J. Ineq. Appl. 281, 1-17, (2013).
18. Mishra, A. K. and Kund, S. N., The second Hankel determinant for a class of analytic functions associated with the Carlson-Shaffer operator, Tamkang J. Math. 44, 73-82, (2013).
19. Noonan, J. W. and Thomas, D. K., On the second Hankel determinant of a really mean p-valent functions, Trans. Amer. Math. Soc. 223, no. 2, 337-346, (1976).
20. Orhan, H., Magesh, N. and Balaji, V. K., Initial coefficient bounds for a general class of bi-univalent functions, Filomat 29, 1259-1267, (2015).
21. Pommerenke, Ch., Univalent Functions, Vandenhoeck and Rupercht, G¨ottingen, (1975).
22. Srivastava, H. M., Eker, S. S., Hamidi, S. G. and Jahangiri, J. M., Faber polynomial coefficient estimates for bi-univalent functions defined by the Tremblay fractional derivative operator, Bull. Iranian Math. Soc. 44, no. 1, 149-157, (2018).
23. Srivastava, H. M., Mishra, A. K. and Gochhayat, P., Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23, 1188-1192, (2010).
24. Wanas, A. K. and Majeed, A. H., Chebyshev polynomial bounded for analytic and bi-univalent functions with respect to symmetric conjugate points, Applied Mathematics E-Notes 19, 14-21, (2019).
25. Wanas, A. K. and Alina, A. L., Applications of Horadam polynomials on Bazileviˇc bi-univalent function satisfying subordinate conditions, Journal of Physics: Conf. Series 1294, 1-6, (2019).
26. Zaprawa, P., On the Fekete-Szego problem for classes of bi-univalent functions, Bull. Belg. Math. Soc. Simon Stevin 21, 169-178,(2014).
27. Zaprawa, P., Estimates of initial coefficients for bi-univalent functions, Abstr. Appl. Anal. 2014, Art. ID 357480, 1-6, (2014).
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2022-12-26
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