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On The Fekete-Szegö Problem for Generalized Class <i>M</i>α,γ(β) Defined By Differential Operator

Year 2016, Volume: 20 Issue: 3, 456 - 459, 11.11.2016

Fethiye Müge Sakar Sultan Aytaş Hatun Özlem Güney

https://doi.org/10.19113/sdufbed.12069

Abstract

In this study the classical Fekete-Szegö problem was investigated. Given f(z)=z+a2z2+a3z3+...  to be an analytic standartly normalized function in the open unit disk U={z ∈ C : |z|<1}. For |a3-μa22|, a sharp maximum value is provided through the classes of S*α,γ(β) order β and type α under the condition of μ≥1.

Keywords

Univalent functions Analytic; Starlike; Convex; Fekete-Szegö problem

References

  • [1] Fekete-Szegö, M. 1933. Eine Bemerkung uber ungrade schlicht funktionen. J. London Math. Soc., 8, 85-89 (in German).
  • [2] Choonweerayoot, A., Thomas, D.K. Upakarnitikaset, W. 1991. On the coefficients of close-to convex functions. Math. Japon, 36 (5),819–826.
  • [3] Keogh, F.R., Merkes, E.P. 1969. A coefficient inequality for certain classes of analytic functions.Proc. Am. Math. Soc.,20,8–12 .
  • [4] Srivastava, H.M., Mıshra, A.K., Das, M.K. 2000. The Fekete-Szegö problem for a subclass of close-to convex function.Complex Variables,44,145–163.
  • [5] Abdel-Gawad, H.R., Thomas, D.K. 1991. A subclass of close-to convex functions. Publ. Inst. Math. (Beograd) (NS),49 (63), 61–66.
  • [6] Abdel-Gawad, H.R., Thomas, D.K. 1992. The Fekete-Szegö problem for strongly close-to convex functions.Proc.Am. Math. Soc.,114 (2),345–349 .
  • [7] Nasr, M.A., El-Gawad, H.R. 1991. On the Fekete-Szegö problem for close-to convex functions of order ρ. In: New Trends in Geometric Function Theory and Applications (Madras 1990), World Science Publishing, River Edge, NJ, 66–74.
  • [8] Darus, M., Thomas, D.K. 1996. On the Fekete-Szegö theorem for close-to convex functions. Math. Japon, 44 (3),507-511.
  • [9] Darus, M., Thomas, D.K. 1998. On the Fekete-Szegö theorem for close-to convex functions. Math. Japon, 47 (1), 125-132.
  • [10] Goel, R.M.,Mehrok, B.S. 1991. A coefficient inequality for certain classes of analytic functions. Tamkang J. Math., 22 (2), 153-163.
  • [11] London, R.R.1993. Fekete-Szegö inequalities for close-to-convex functions. Proc. Am. Math. Soc.,117 (4),947–950.
  • [12] Trimble, S.Y. 1975. A coefficient inequality for convex univalent functions. Proc. Am. Math. Soc.,48, 266–267.
  • [13] Koepf, W. 1987. On the Fekete-Szegö problem for close-to convex functions. II. Arch. Math. (Basel),49 (5), 420–433.
  • [14] Koepf, W. 1987. On the Fekete-Szegö problem for close-to convex functions. Proc. Am. Math. Soc.,101 (1), 89–95.
  • [15] Altınkaya, Ş., Yalçın, S. 2014. Fekete-Szegö Inequalities for Certain Classes of Bi-univalent Functions.International Scholarly Research Notices,Volume, Article ID 327962, 6 pages.
  • [16] Altınkaya, Ş., Yalçın, S. 2014. Fekete-Szegö Inequalities for Classes of Bi-univalent Functions defined by subordination. Advances in Mathematics: Scientific Journal, 3 (2),63-71.
  • [17] Sokół, J.,Raina, R.K., Yilmaz Özgür, N.2015. Applications of k-Fibonacci numbers for the starlike analytic functions.Hacet. J. Math. Stat., 44(1), 121-127.
  • [18] Nalinakshi, L., Parvatham, R. 1995. On Salagean-Pascu Type of Generalised Sakaguchi Class of Functions. Kyungpook Math.J., 35, 1-15.
  • [19] Salagean, G.S. 1981. Subclasses of univalent funtions. Lecture notes in Mathematics Springer Verlag, 1013, 363-372.
  • [20] Kaplan, W. 1952. Close-to convex schlicht functions. Michigan Math. J.,1,169–185.
  • [21] Pommerenke, Ch. 1975. Univalent Functions.With a chapter on quadratic differentials by Gerd Jensen.StudiaMathematica/MathematischeLehrbucher,BandXXV,Vandenheck&Ruprecht. Göttingen, MR 58#22526.Zbl 298.30014.
  • [22] Jahangiri, M.1995. A coefficient inequality for a class of close-to convex functions. Math. Japon, 41 (3), 557-559.
  • [23] Orhan, H., Kamali, M. 2003. On the Fekete-Szegö problem. Applied Mathematics and Computation, 144, 181-186.
  • [24] Frasin, B.A., Darus, M. 2000. On the Fekete-Szegö problem. Internet J. Math. Sci., 24 (9), 577-581.

Year 2016, Volume: 20 Issue: 3, 456 - 459, 11.11.2016

Fethiye Müge Sakar Sultan Aytaş Hatun Özlem Güney

https://doi.org/10.19113/sdufbed.12069

Abstract

References

  • [1] Fekete-Szegö, M. 1933. Eine Bemerkung uber ungrade schlicht funktionen. J. London Math. Soc., 8, 85-89 (in German).
  • [2] Choonweerayoot, A., Thomas, D.K. Upakarnitikaset, W. 1991. On the coefficients of close-to convex functions. Math. Japon, 36 (5),819–826.
  • [3] Keogh, F.R., Merkes, E.P. 1969. A coefficient inequality for certain classes of analytic functions.Proc. Am. Math. Soc.,20,8–12 .
  • [4] Srivastava, H.M., Mıshra, A.K., Das, M.K. 2000. The Fekete-Szegö problem for a subclass of close-to convex function.Complex Variables,44,145–163.
  • [5] Abdel-Gawad, H.R., Thomas, D.K. 1991. A subclass of close-to convex functions. Publ. Inst. Math. (Beograd) (NS),49 (63), 61–66.
  • [6] Abdel-Gawad, H.R., Thomas, D.K. 1992. The Fekete-Szegö problem for strongly close-to convex functions.Proc.Am. Math. Soc.,114 (2),345–349 .
  • [7] Nasr, M.A., El-Gawad, H.R. 1991. On the Fekete-Szegö problem for close-to convex functions of order ρ. In: New Trends in Geometric Function Theory and Applications (Madras 1990), World Science Publishing, River Edge, NJ, 66–74.
  • [8] Darus, M., Thomas, D.K. 1996. On the Fekete-Szegö theorem for close-to convex functions. Math. Japon, 44 (3),507-511.
  • [9] Darus, M., Thomas, D.K. 1998. On the Fekete-Szegö theorem for close-to convex functions. Math. Japon, 47 (1), 125-132.
  • [10] Goel, R.M.,Mehrok, B.S. 1991. A coefficient inequality for certain classes of analytic functions. Tamkang J. Math., 22 (2), 153-163.
  • [11] London, R.R.1993. Fekete-Szegö inequalities for close-to-convex functions. Proc. Am. Math. Soc.,117 (4),947–950.
  • [12] Trimble, S.Y. 1975. A coefficient inequality for convex univalent functions. Proc. Am. Math. Soc.,48, 266–267.
  • [13] Koepf, W. 1987. On the Fekete-Szegö problem for close-to convex functions. II. Arch. Math. (Basel),49 (5), 420–433.
  • [14] Koepf, W. 1987. On the Fekete-Szegö problem for close-to convex functions. Proc. Am. Math. Soc.,101 (1), 89–95.
  • [15] Altınkaya, Ş., Yalçın, S. 2014. Fekete-Szegö Inequalities for Certain Classes of Bi-univalent Functions.International Scholarly Research Notices,Volume, Article ID 327962, 6 pages.
  • [16] Altınkaya, Ş., Yalçın, S. 2014. Fekete-Szegö Inequalities for Classes of Bi-univalent Functions defined by subordination. Advances in Mathematics: Scientific Journal, 3 (2),63-71.
  • [17] Sokół, J.,Raina, R.K., Yilmaz Özgür, N.2015. Applications of k-Fibonacci numbers for the starlike analytic functions.Hacet. J. Math. Stat., 44(1), 121-127.
  • [18] Nalinakshi, L., Parvatham, R. 1995. On Salagean-Pascu Type of Generalised Sakaguchi Class of Functions. Kyungpook Math.J., 35, 1-15.
  • [19] Salagean, G.S. 1981. Subclasses of univalent funtions. Lecture notes in Mathematics Springer Verlag, 1013, 363-372.
  • [20] Kaplan, W. 1952. Close-to convex schlicht functions. Michigan Math. J.,1,169–185.
  • [21] Pommerenke, Ch. 1975. Univalent Functions.With a chapter on quadratic differentials by Gerd Jensen.StudiaMathematica/MathematischeLehrbucher,BandXXV,Vandenheck&Ruprecht. Göttingen, MR 58#22526.Zbl 298.30014.
  • [22] Jahangiri, M.1995. A coefficient inequality for a class of close-to convex functions. Math. Japon, 41 (3), 557-559.
  • [23] Orhan, H., Kamali, M. 2003. On the Fekete-Szegö problem. Applied Mathematics and Computation, 144, 181-186.
  • [24] Frasin, B.A., Darus, M. 2000. On the Fekete-Szegö problem. Internet J. Math. Sci., 24 (9), 577-581.
There are 24 citations in total.

Details

Journal Section Makaleler
Authors

Fethiye Müge Sakar This is me

Sultan Aytaş This is me

Hatun Özlem Güney

Publication Date November 11, 2016
Published in Issue Year 2016 Volume: 20 Issue: 3

Cite

APA Sakar, F. M., Aytaş, S., & Güney, H. Ö. (2016). On The Fekete-Szegö Problem for Generalized Class Mα,γ(β) Defined By Differential Operator. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 20(3), 456-459. https://doi.org/10.19113/sdufbed.12069
AMA Sakar FM, Aytaş S, Güney HÖ. On The Fekete-Szegö Problem for Generalized Class Mα,γ(β) Defined By Differential Operator. J. Nat. Appl. Sci. December 2016;20(3):456-459. doi:10.19113/sdufbed.12069
Chicago Sakar, Fethiye Müge, Sultan Aytaş, and Hatun Özlem Güney. “On The Fekete-Szegö Problem for Generalized Class Mα,γ(β) Defined By Differential Operator”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20, no. 3 (December 2016): 456-59. https://doi.org/10.19113/sdufbed.12069.
EndNote Sakar FM, Aytaş S, Güney HÖ (December 1, 2016) On The Fekete-Szegö Problem for Generalized Class Mα,γ(β) Defined By Differential Operator. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20 3 456–459.
IEEE F. M. Sakar, S. Aytaş, and H. Ö. Güney, “On The Fekete-Szegö Problem for Generalized Class Mα,γ(β) Defined By Differential Operator”, J. Nat. Appl. Sci., vol. 20, no. 3, pp. 456–459, 2016, doi: 10.19113/sdufbed.12069.
ISNAD Sakar, Fethiye Müge et al. “On The Fekete-Szegö Problem for Generalized Class Mα,γ(β) Defined By Differential Operator”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20/3 (December 2016), 456-459. https://doi.org/10.19113/sdufbed.12069.
JAMA Sakar FM, Aytaş S, Güney HÖ. On The Fekete-Szegö Problem for Generalized Class Mα,γ(β) Defined By Differential Operator. J. Nat. Appl. Sci. 2016;20:456–459.
MLA Sakar, Fethiye Müge et al. “On The Fekete-Szegö Problem for Generalized Class Mα,γ(β) Defined By Differential Operator”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol. 20, no. 3, 2016, pp. 456-9, doi:10.19113/sdufbed.12069.
Vancouver Sakar FM, Aytaş S, Güney HÖ. On The Fekete-Szegö Problem for Generalized Class Mα,γ(β) Defined By Differential Operator. J. Nat. Appl. Sci. 2016;20(3):456-9.
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