ON THE FEKETE-SZEGÖ PROBLEM FOR ANALYTIC FUNCTIONS DEFINED BY USING SYMMETRIC $Q$-DERIVATIVE OPERATOR

Year 2017, Volume: 5 Issue: 1, 176 - 186, 03.04.2017

Şahsene Altınkaya , Sibel Yalçın

Abstract

The aim of this paper is to establish the Fekete-Szego inequalities for two new subclasses of analytic functions which are associated with symmetric $q$-derivative operator.

Keywords

Analytic functions, bi-univalent functions, Fekete-Szego functional, q-derivative operator.

References

• [1] S. Altinkaya and S. Yalcin, Fekete-Szego inequalities for classes of bi-univalent functions dened by subordination, Advances in Mathematics: Scientic Journal, Vol:3, No.2 (2014), 63-71.
• [2] M. K. Aouf, R. M. El-Ashwah, A. M. Hassan and A. H. Hassan, Fekete-Szego problem for a new class of analytic functions dened by using a generalized differential operator, Acta Universitatis Palackianae Olomucensis, Facultas Rerum Naturalium Mathematica, Vol:52, No.1 (2013), 21-34.
• [3] K. L. Brahim and Y. Sidomou, On some symmetric q-special functions, Le Matematiche, Vol:LXVIII (2013), 107{122.
• [4] L.C. Biedenharn, The Quantum Group SU(2)(q) and a q-Analogue of the Boson Operators, J. Phys. A Vol: 22 (1984), L873-L878.
• [5] R. Bucur, L. Andrei and D. Breaz, Coeffient bounds and Fekete-Szego problem for a class of analytic functions dened by using a new differential operator, Applied Mathematical Sciences, Vol:9, No.28 (2015), 1355 - 1368.
• [6] Duren, P. L., Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Springer, New York, USA, 259, 1983.
• [7] M. Fekete and G. Szego, Eine Bemerkung uber ungerade schlichte Funktionen, J. Lond. Math. Soc. Vol:8, (1933), 85-89.
• [8] Gasper, G. and Rahman, M., Basic Hypergeometric Series (with a Foreword by Richard Askey), Encyclopedia of Mathematics and Its Applications, Vol:35, Cambridge University Press, Cambridge, New York, Port Chester, Melbourne and Sydney, 1990; Second edition, Encyclopedia ofMathematics and Its Applications, Vol:96, Cambridge University Press, Cambridge, London and New York, 2004.
• [9] F. H. Jackson, On q-functions and a certain difference operator, Transactions of the Royal Society of Edinburgh, Vol:46 (1908), 253-281.
• [10] B. Kowalczyk and A. Lecko, Fekete-Szego problem for a certain subclass of close-to-convex functions, Bull. Malays. Math. Sci. Soc. Vol:38 (2015), 1393-1410.
• [11] Ma, W. and Minda, D., A unied treatment of some special classes of univalent functions, in: Proceedings of the Conference on Complex Analysis, Z. Li, F. Ren, L. Yang, and S. Zhan (Eds.), Int. Press (1994), 157-169.
• [12] Pommerenke, C., Univalent Functions, Vandenhoeck & Ruprecht, Gottingen, 1975.
• [13] T. M. Seoudy, Fekete-Szego problems for certain class of nonBazilevic functions involving the Dziok- Srivastava operator, Romai J. Vol:10, No.1 (2014), 175-186.
• [14] Srivastava, H.M., Univalent functions, fractional calculus, and associated generalized hypergeometric functions, in Univalent Functions; Fractional Calculus; and Their Applications (H. M. Srivastava and S. Owa, Editors), Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1989.
• [15] H M. Srivastava, A. K. Mishra and P. Gochhayat, Certain subclasses of analytic and biunivalent functions, Appl. Math. Lett. Vol:23 (2010), 1188{1192.