Some new subclasses of bi-univalent functions

Authors

  • Saurabh PORWAL Department of Mathematics U.I.E.T., C.S.J.M. University Kanpur-208024, (U.P.), India e-mail: saurabhjcb@rediffmail.com https://orcid.org/0000-0003-0847-3550
  • Sanjay Kumar GHAI Principal, BVM College of Technology and Management Gwalior-474001, (M.P.), India e-mail: sanjaykumarghai@yahoo.com
  • Kaushal KUMAR Department of Mathematics U.I.E.T., C.S.J.M. University Kanpur-208024, (U.P.), India

Keywords:

Univalent functions, bi-univalent functions, subordination, Salagean derivative.

Abstract

The purpose of the present paper is to obtain the initial coeffcients for normalized analytic functions f in the open unit disk U with its inverse g …

... Relevant connections of the results presented here with various known results are briefly indicated. Finally, we give an open problem for the readers.

Mathematics Subject Classification (2010): 30C45.

References

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

Branna, D.A., Taha, T.S., On some classes of bi-univalent functions, Studia Univ. Babes-Bolyai Math., 31(1986), no. 2, 70-77.

Brannan, D.A., Clunie, J., Kirwan, W.E., Coefficient estimates for a class of starlike functions, Canad. J. Math., 22(1970), 476-485.

Duren, P.L., Univalent functions, In: Grundlehred der Mathematischen Wissenschaften, vol. 259, Springer, New York, 1983.

Frasin, B.A., Aouf, M.K., New subclasses of bi-univalent functions, Appl. Math. Lett., 24(2011), no. 9, 1569-1573.

Goyal, S.P., Goswami, P., Estimate for initial Maclaurin coefficients of bi-univalent functions for a class defined by fractional derivatives, J. Egypt. Math. Soc., 20(2012), no. 3, 179-182.

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

Ma, W.C., Minda, D., A unified treatment of some special classes of univalent functions, In: Proceedings of the Conference on Complex Analysis, Tianjin, 1992, 157-169, Conf. Proc. Lecture Notes Anal. L. Int. Press, Cambridge, MA, 1994.

Netanyahu, E., The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in jzj < 1, Arch. Ration. Mech. Anal., 32(1969), 100-112.

Porwal, S., Darus, M., On a new subclass of Bi-univalent functions, J. Egypt. Math. Soc., 21(2013), 190-193.

Salagean, G.S., Subclasses of univalent functions, Complex Analysis-Fifth Romanian Finish Seminar, Bucharest, 1(1983), 362-372.

Srivastava, H.M., Mishra, A.K., Gochhayat, P., Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., 23(2010), no. 10, 1188-1192.

Xu, Q.H., Gui, Y.C., Srivastava, H.M., Coefficient estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett., 25(2012), 990-994.

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Published

2015-12-30

How to Cite

PORWAL, S., GHAI, S. K., & KUMAR, K. (2015). Some new subclasses of bi-univalent functions. Studia Universitatis Babeș-Bolyai Mathematica, 60(4), 543–552. Retrieved from https://studia.reviste.ubbcluj.ro/index.php/subbmathematica/article/view/5830

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