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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

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.

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

Abstract

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.
There are 15 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

Şahsene Altınkaya

Sibel Yalçın

Publication Date April 3, 2017
Submission Date April 1, 2017
Acceptance Date January 25, 2017
Published in Issue Year 2017 Volume: 5 Issue: 1

Cite

APA Altınkaya, Ş., & Yalçın, S. (2017). ON THE FEKETE-SZEGÖ PROBLEM FOR ANALYTIC FUNCTIONS DEFINED BY USING SYMMETRIC $Q$-DERIVATIVE OPERATOR. Konuralp Journal of Mathematics, 5(1), 176-186.
AMA Altınkaya Ş, Yalçın S. ON THE FEKETE-SZEGÖ PROBLEM FOR ANALYTIC FUNCTIONS DEFINED BY USING SYMMETRIC $Q$-DERIVATIVE OPERATOR. Konuralp J. Math. April 2017;5(1):176-186.
Chicago Altınkaya, Şahsene, and Sibel Yalçın. “ON THE FEKETE-SZEGÖ PROBLEM FOR ANALYTIC FUNCTIONS DEFINED BY USING SYMMETRIC $Q$-DERIVATIVE OPERATOR”. Konuralp Journal of Mathematics 5, no. 1 (April 2017): 176-86.
EndNote Altınkaya Ş, Yalçın S (April 1, 2017) ON THE FEKETE-SZEGÖ PROBLEM FOR ANALYTIC FUNCTIONS DEFINED BY USING SYMMETRIC $Q$-DERIVATIVE OPERATOR. Konuralp Journal of Mathematics 5 1 176–186.
IEEE Ş. Altınkaya and S. Yalçın, “ON THE FEKETE-SZEGÖ PROBLEM FOR ANALYTIC FUNCTIONS DEFINED BY USING SYMMETRIC $Q$-DERIVATIVE OPERATOR”, Konuralp J. Math., vol. 5, no. 1, pp. 176–186, 2017.
ISNAD Altınkaya, Şahsene - Yalçın, Sibel. “ON THE FEKETE-SZEGÖ PROBLEM FOR ANALYTIC FUNCTIONS DEFINED BY USING SYMMETRIC $Q$-DERIVATIVE OPERATOR”. Konuralp Journal of Mathematics 5/1 (April 2017), 176-186.
JAMA Altınkaya Ş, Yalçın S. ON THE FEKETE-SZEGÖ PROBLEM FOR ANALYTIC FUNCTIONS DEFINED BY USING SYMMETRIC $Q$-DERIVATIVE OPERATOR. Konuralp J. Math. 2017;5:176–186.
MLA Altınkaya, Şahsene and Sibel Yalçın. “ON THE FEKETE-SZEGÖ PROBLEM FOR ANALYTIC FUNCTIONS DEFINED BY USING SYMMETRIC $Q$-DERIVATIVE OPERATOR”. Konuralp Journal of Mathematics, vol. 5, no. 1, 2017, pp. 176-8.
Vancouver Altınkaya Ş, Yalçın S. ON THE FEKETE-SZEGÖ PROBLEM FOR ANALYTIC FUNCTIONS DEFINED BY USING SYMMETRIC $Q$-DERIVATIVE OPERATOR. Konuralp J. Math. 2017;5(1):176-8.
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