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

Yıl 2017, Cilt: 5 Sayı: 1, 176 - 186, 03.04.2017

Öz

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.

Kaynakça

  • [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.
Yıl 2017, Cilt: 5 Sayı: 1, 176 - 186, 03.04.2017

Öz

Kaynakça

  • [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.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Konular Mühendislik
Bölüm Articles
Yazarlar

Şahsene Altınkaya

Sibel Yalçın

Yayımlanma Tarihi 3 Nisan 2017
Gönderilme Tarihi 1 Nisan 2017
Kabul Tarihi 25 Ocak 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 5 Sayı: 1

Kaynak Göster

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. Nisan 2017;5(1):176-186.
Chicago Altınkaya, Şahsene, ve Sibel Yalçın. “ON THE FEKETE-SZEGÖ PROBLEM FOR ANALYTIC FUNCTIONS DEFINED BY USING SYMMETRIC $Q$-DERIVATIVE OPERATOR”. Konuralp Journal of Mathematics 5, sy. 1 (Nisan 2017): 176-86.
EndNote Altınkaya Ş, Yalçın S (01 Nisan 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 ve S. Yalçın, “ON THE FEKETE-SZEGÖ PROBLEM FOR ANALYTIC FUNCTIONS DEFINED BY USING SYMMETRIC $Q$-DERIVATIVE OPERATOR”, Konuralp J. Math., c. 5, sy. 1, ss. 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 (Nisan 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 ve Sibel Yalçın. “ON THE FEKETE-SZEGÖ PROBLEM FOR ANALYTIC FUNCTIONS DEFINED BY USING SYMMETRIC $Q$-DERIVATIVE OPERATOR”. Konuralp Journal of Mathematics, c. 5, sy. 1, 2017, ss. 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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