An Unified Approach to Second Hankel Determinant of Bi-Subordinate Functions

1. Ali, R.M., Lee, S.K., Ravichandran, V., Subramaniam, S.: Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions. Appl. Math. Lett. 25, 344–351 (2012)

   Article  MathSciNet  MATH  Google Scholar 

2. Altinkaya, Ş., Yalçın, S.: Upper bound of Second Hankel determinant for Bi-Bazilevic̆ functions. Mediterr. J. Math. 13, 4081–4090 (2016)

   Article  MathSciNet  MATH  Google Scholar 

3. Altinkaya, Ş., Yalçın, S.: Faber polynomial coefficient bounds for a subclass of bi-univalent functions. C. R. Acad. Sci. Paris Ser. I(353), 1075–1080 (2015)

   Article  MathSciNet  MATH  Google Scholar 

4. Brannan, D.A., Clunie, J.: Aspects of contemporary complex analysis. In: Proceedings of the NATO Advanced Study Institute Held at University of Durham. Academic, New York (1979)

5. Cantor, D.G.: Power series with integral coefficients. Bull. Am. Math. Soc. 69, 362–366 (1963)

   Article  MathSciNet  MATH  Google Scholar 

6. Deniz, E.: Çağlar and H. Orhan, Second Hankel determinant for bi-starlike and bi-convex functions of order \(\beta \). Appl. Math. Comput. 271, 301–307 (2015)

   MathSciNet  Google Scholar 

7. Hamidi, S.G., Jahangiri, J.M.: Faber polynomial coefficients of bi-subordinate functions. C. R. Math. Acad. Sci. Paris. 354, 365–370 (2016)

   Article  MathSciNet  Google Scholar 

8. Fekete, M., Szegö, G.: Eine Bemerkung Uber Ungerade Schlichte Funktionen. J. Lond. Math. Soc. 8, 85–89 (1933)

   Article  MathSciNet  MATH  Google Scholar 

9. Frasin, B.A., Aouf, M.K.: New subclasses of bi-univalent functions. Appl. Math. Lett. 24, 1569–1573 (2011)

   Article  MathSciNet  MATH  Google Scholar 

10. Duren, P.L.: Univalent Functions, Grundlehren der Mathematischen Wissenschaften, vol. 259. Springer, New York (1983)

    Google Scholar 

11. Grenander, U., Szegö, G.: Toeplitz forms and their applications. California Monographs in Mathematical Sciences Univ, California Press, Berkeley (1958)

12. Hamidi, S.G., Halim, S.A., Jahangiri, J.M.: Jahangiri, Coefficient estimates for a class of meromorphic bi-univalent functions. C. R. Math. Acad. Sci. Paris, Ser. I. 351, 349–352 (2013)

    Article  MATH  Google Scholar 

13. Jahangiri, J. M., Hamidi, S. G.: Coefficient estimates for certain classes of bi-univalent functions. Int. J. Math. Math. Sci. Article ID 190560, 4 (2013)

14. Jahangiri, J.M., Hamidi, S.G., Halim, S.A.: Coefficients of bi-univalent functions with positive real part derivatives. Bull. Malays. Math. Sci. Soc. 37, 633–640 (2014)

    MathSciNet  MATH  Google Scholar 

15. Kanas, S.: An unified approach to the Fekete-Szegö problem. Appl. Math. Comput. 218, 8453–8461 (2012)

    MathSciNet  MATH  Google Scholar 

16. Kanas, S., Kim, S.-A., Sivasubramanian, S.: Verification of Brannan and Clunie’s conjecture for certain subclasses of bi-univalent function. Ann. Polonici Mathematici. 113, 295–304 (2015)

    Article  MathSciNet  MATH  Google Scholar 

17. Kanas, S., Darwish, H.E.: Fekete-Szegö problem for starlike and convex functions of complex order. Appl. Math. Lett. 23, 777–782 (2010)

    Article  MathSciNet  MATH  Google Scholar 

18. Kedzierawski, A.W.: Some remarks on bi-univalent functions. Ann. Univ. Mariae Curie-Sk lodowska Sect. A. 39, 77–81 (1985)

    MathSciNet  MATH  Google Scholar 

19. Lewin, M.: On a coefficient problem for bi-univalent functions. Proc. Am. Math. Soc. 18, 63–68 (1967)

    Article  MathSciNet  MATH  Google Scholar 

20. Li, X.-F., Wang, A.-P.: Two new subclasses of bi-univalent functions. Int. Math. Forum. 7, 1495–1504 (2012)

    MathSciNet  MATH  Google Scholar 

21. Noonan, J.W., Thomas, D.K.: On the second Hankel determinant of areally mean p-valent functions. Trans. Am. Math. Soc. 223, 337–346 (1976)

    MathSciNet  MATH  Google Scholar 

22. Orhan, H., Magesh, N., Yamini, J.: Bounds for the second Hankel determinant of certain bi-univalent functions. Turk. J. Math. 40, 679–687 (2016)

    Article  MathSciNet  Google Scholar 

23. Srivastava, H.M., Mishra, A.K., Gochhayat, P.: Certain subclasses of analytic and biunivalent functions. Appl. Math. Lett. 23, 1188–1192 (2010)

    Article  MathSciNet  MATH  Google Scholar 

24. Pommerenke, C.: Univalent Functions. Vandenhoeck and Ruprecht, Göttingen (1975)

25. Zaprawa, P.: On the Fekete-Szegö problem for classes of bi-univalent functions. Bull. Belg. Math. Soc. Simon Stevin. 21, 169–178 (2014)

    MathSciNet  MATH  Google Scholar 

26. Zaprawa, P.: Estimates of initial coefficients for bi-univalent functions. Abstr. Appl. Anal. Art. ID 357480, 1–6 (2014)

27. Zireh, A., Analouei Adegani, E.: Coefficient estimates for a subclass of analytic and bi-univalent functions. Bull. Iran. Math. Soc. 42, 881–889 (2016)

    MathSciNet  MATH  Google Scholar 

28. Zireh, A., Analouei Adegani, E., Bulut, S.: Faber polynomial coefficient estimates for a comprehensive subclass of analytic bi-univalent functions defined by subordination. Bull. Belg. Math. Soc. Simon Stevin. 23, 487–504 (2016)

29. Zireh, A., Analouei Adegani, E., Bidkham, M.: Faber polynomial coefficient estimates for subclass of bi-univalent functions defined by quasi-subordinate. Mathematica Slovaca (in Press)

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