ESTIMATE FOR INITIAL MACLAURIN COEFFICIENTS OF SUBCLASS OF BI-UNIVALENT FUNCTIONS INVOLVING THE Q- DERIVATIVE OPERATOR

In this paper, estimates for second and third MacLaurin coefficients of a new subclass of analytic and bi-univalent functions in the open unit disk are determined, and certain special cases are also indicated

___

  • A. Aral, V. Gupta and R.P.Agrawal, Applications of q-calculus in Operator Theory, Springer, New York, USA, 2013.
  • D. A. Brannan and T. S. Taha, On some classes of bi-univalent functions, Stud. Univ. Babe¸s- Bolyai Math., 31(1986), no. 2, 70–77.
  • P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften Series, , Springer Verlag, New York, 1983.
  • B. A. Frasin and M. K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett., (2011), no. 9, 1569–1573.
  • S. P. Goyal and P. Goswami, Estimate for initial Maclaurin coe¢ cients of bi-univalent func- tions for a class de…ned by fractional derivatives, J. Egyptian Math. Soc., 20(3)(2012), 179–
  • F. H. Jackson, On q-de…nite integrals, Quarterly J. Pure Appl. Math. 41 (1910), 193-203.
  • F. H. Jackson, On q-functions and a certain diğerence operator, Transactions of the Royal Society of Edinburgh 46 (1908), 253-281.
  • V. Paatero, Uber die konforme Abbildung von Gebieten deren Rander von beschrÃxonkter Drehung sind, Ann. Acad. Sci. Fenn. Ser. A33 No. 9 (1931).
  • K. Padmanabhan and R. Parvatham, Properties of a class of functions with bounded bound- ary rotation, Ann. Polon. Math., 31(1975), 311–323.
  • B. Pinchuk, Functions with bounded boundary rotation, Israel J. Math., 10(1971), 7–16.
  • H. M. Srivastava, A. K. Mishra and P. Gochhayat, Certain subclasses of analytic and bi- univalent functions, Appl. Math. Lett., 23(2010), no. 10, 1188–1192.
  • Q.-H. Xu, Y.-C. Gui and H.M. Srivastava, Coe¢ cient estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett.25 (2012) 990-994.
  • Q.-H. Xu, H.-G. Xiao and H.M. Srivastava, A certain general subclass of analytic and biu- nivalent functions and associated coe¢ cient estimate problems, Appl. Math. Comput. 218 (2012) 11461165.