Initial coefficients for a subclass of bi-univalent functions defined by Salagean differential operator

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  • R. M. Ali, S. K. Lee, V. Ravichandran and S. Supramaniam, Coe¢ cient estimates for bi- univalent Ma-Minda starlike and convex functions, Appl. Math. Lett. 25 (3) (2012), 344–351. [2] D. A. Brannan, J.G. Clunie (Eds.), Aspects of Contemporary Complex Analysis (Proceedings of the NATO Advanced Study Institute held at the University of Durham, Durham; July 1 20, 1979), Academic Press, New York and London, 1980.
  • D. A. Brannan and T.S. Taha, On some classes of bi-univalent functions, in: S.M. Mazhar, A. Hamoui, N.S. Faour (Eds.), Math. Anal. and Appl., Kuwait; February 18–21, 1985, in: KFAS Proceedings Series, vol. 3, Pergamon Press, Elsevier Science Limited, Oxford, 1988, pp. 53–60. see also Studia Univ. Babe¸s-Bolyai Math. 31 (2) (1986), 70–77.
  • S. Bulut, Faber polynomial coe¢ cient estimates for a comprehensive subclass of analytic bi-univalent functions, C. R. Acad. Sci. Paris, Ser. I, 352 (6) (2014), pp. 479–484.
  • S. Bulut, N. Magesh and V. K. Balaji, Faber polynomial coe¢ cient estimates for certain subclasses of meromorphic bi-univalent functions, Comptes Rendus Mathematique 353(2) (2015), 113-116.
  • M. Ça¼glar, H. Orhan and N. Ya¼gmur, Coe¢ cient bounds for new subclasses of bi-univalent functions, Filomat 27(7) (2013), 1165-1171.
  • E. Deniz, Certain subclasses of bi-univalent functions satisfying subordinate conditions, J. Class. Anal. 2(1) (2013), 49–60.
  • P. L. Duren, Univalent functions,Grundlehren der Mathematischen Wissenschaften, 259, Springer, New York, 1983.
  • B. A. Frasin, M.K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett. 24 (2011), 1569-1573.
  • S. G. Hamidi, J. M. Jahangiri, Faber polynomial coe¢ cient estimates for analytic bi-close- to-convex functions, C. R. Acad. Sci. Paris, Ser. I 352 (2014), 17–20.
  • A. W. Kedzierawski, Some remarks on bi-univalent functions, Ann. Univ.Mariae Curie- Skğodowska Sect. A 39 (1985), 77–81 (1988).
  • S. Sivaprasad Kumar, V. Kumar and V. Ravichandran, Estimates for the initial coe¢ cients of bi-univalent functions, Tamsui Oxford J. Inform. Math. Sci. 29(4) (2013), 487-504.
  • M. Lewin, On a coe¢ cient problem for bi-univalent functions, Proc. Amer. Math. Soc. 18 (1967), 63–68.
  • A. K. Mishra and S. Barık, Estimates for the initial coe¢ cients of bi-univalent
  • convex analytic functions in the unit disc, Journal of Classical Analysis, 7(1) (2015), 73-81.
  • E. Netanyahu, The minimal distance of the image boundary from the origin and the second coe¢ cient of a univalent function in jzj < 1, Arch. Rational Mech. Anal. 32 (1969), 100-112. [16] H. Orhan, N. Magesh and V. K. Balaji, Initial coe¢ cient bounds for a general class of bi- univalent functions, Filomat 29(6) (2015), 1259–1267.
  • C. Ramachandran, R. Ambrose Prabhu and N. Magesh, Initial coe¢ cient estimates for certain subclasses of bi-univalent functions of Ma-Minda type, Applied Mathematical Sciences, 9(47) (2015), 2299-2308.
  • G. S. Salagean, Subclasses of univalent functions, Complex analysis - Proc. 5th Rom.-Finn. Semin., Bucharest 1981, Part 1, Lect. Notes Math., 1013 (1983), 362–372.
  • H. M. Srivastava, A. K. Mishra, P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010), 1188–1192.
  • H. M. Srivastava, S. Bulut, M. Ça¼glar, N. Ya¼gmur, Coe¢ cient estimates for a general subclass of analytic and bi-univalent functions, Filomat 27(5) (2013), 831-842.
  • H. M. Srivastava and D. Bansal, Coe¢ cient estimates for a subclass of analytic and bi- univalent functions, Journal of the Egyptian Mathematical Society 23(2) (2015), 242-246.
  • Y. Sun, Y. P. Jiang and A. Rasila, Coe¢ cient estimates for certain subclasses of analytic and bi-univalent functions, Filomat 29(2) (2015), 351-360.
  • D. L. Tan, Coe¢ cient estimates for bi-univalent functions, Chinese Ann. Math. Ser. A 5 (5) (1984), 559–568.
  • P. Zaprawa, Estimates of initial coe¢ cients for bi-univalent functions, Abstr. Appl. Anal., 2014, Article ID 357480, 6 pages.