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Coefficient bounds for new subclasses of bi-univalent functions

Yıl 2016, Cilt: 4 Sayı: 3, 197 - 203, 30.09.2016

Öz



In the present paper, introduction of new subclasses
of bi-univalent functions in the open disk was defined. Moreover,by using
Salagean operator,in these new subclasses for functions, upper bounds for the
second and third coefficients were found. Presented results are a
generalization of the results obtained by Srivastava et al.[12], Frasin and
Aouf [7] and Çağlar et al.[5].




Kaynakça

  • Altankaya Ş., Yalçın S., Faber polynomial coefficient bounds for a subclass of bi-univalent functions, Stud. Univ. Babeş-Bolyai Math. 61 (1) (2016) 37-44.
  • Altankaya Ş., Yalçın S., Faber polynomial coefficient bounds for a subclass of bi-univalent functions, C. R. Acad. Sci. Paris, Ser. I 353 (12) (2015) 1075-1080.
  • Ali R.M., Lee S.K., Ravichandran V. , Supramaniam S., Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions, Applied Mathematics Letters, 25 (2012) 344-351.
  • Brannan D.A., Taha T.S., On some classes of bi-univalent functions, in: S.M. Mazhar, A. Hamoui, N.S. Faour (Eds.), Mathematical Analysis and Its Applications, Kuwait; February 18-21, 1985, in: KFAS Proceedings Series, vol. 3, Pergamon Press, Elsevier Science Limited, Oxford, 1988, pp. 53-60. See also Studia Univ. Babeş-Bolyai Math. 31 (2) (1986) 70-77.
  • Çağlar M., Orhan H. and Yağmur N., Coefficient bounds for new subclasses of bi-univalent functions, Filomat 27(7) (2013),1165-1171.
  • Duren P.L., Univalent Functions, in: Grundlehren der Mathematischen Wissenschaften, Band 259, Springer-Verlag, New York, Berlin, Heidelberg and Tokyo, 1983.
  • Frasin B.A. and Aouf M.K., New subclasses of bi-univalent functions, Applied Mathematics Letters, 24 (2011), 1569-1573.
  • Lewin M. , On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc. 18 (1967) 63-68.
  • Netanyahu E., The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in |z|<1, Arch. Rational Mech. Anal. 32 (1969) 100-112.
  • Salagean G.S., Subclasses of univalent functions, Lecture Notes in Math., Springer, Berlin, 1013, 362-372, 1983.
  • Srivastava H. M., Bulut S., Çağlar M., and Yağmur N., a Coefficient estimates for a general subclass of analytic and biunivalent functions, a Filomat, vol. 27, no. 5, pp.831-842, 2013.
  • Srivastava H.M., Mishra A.K. and Gochhayat P., Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010) 1188-1192.
  • Srivastava H.M. , Sümer Eker S. , Ali RM., Coefficient bounds for a certain class of analytic and bi-univalent functions. Filomat 29 (2015) 1839-1845.
  • Taha T.S., Topics in Univalent Function Theory, Ph.D. Thesis, University of London, 1981.
Yıl 2016, Cilt: 4 Sayı: 3, 197 - 203, 30.09.2016

Öz

Kaynakça

  • Altankaya Ş., Yalçın S., Faber polynomial coefficient bounds for a subclass of bi-univalent functions, Stud. Univ. Babeş-Bolyai Math. 61 (1) (2016) 37-44.
  • Altankaya Ş., Yalçın S., Faber polynomial coefficient bounds for a subclass of bi-univalent functions, C. R. Acad. Sci. Paris, Ser. I 353 (12) (2015) 1075-1080.
  • Ali R.M., Lee S.K., Ravichandran V. , Supramaniam S., Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions, Applied Mathematics Letters, 25 (2012) 344-351.
  • Brannan D.A., Taha T.S., On some classes of bi-univalent functions, in: S.M. Mazhar, A. Hamoui, N.S. Faour (Eds.), Mathematical Analysis and Its Applications, Kuwait; February 18-21, 1985, in: KFAS Proceedings Series, vol. 3, Pergamon Press, Elsevier Science Limited, Oxford, 1988, pp. 53-60. See also Studia Univ. Babeş-Bolyai Math. 31 (2) (1986) 70-77.
  • Çağlar M., Orhan H. and Yağmur N., Coefficient bounds for new subclasses of bi-univalent functions, Filomat 27(7) (2013),1165-1171.
  • Duren P.L., Univalent Functions, in: Grundlehren der Mathematischen Wissenschaften, Band 259, Springer-Verlag, New York, Berlin, Heidelberg and Tokyo, 1983.
  • Frasin B.A. and Aouf M.K., New subclasses of bi-univalent functions, Applied Mathematics Letters, 24 (2011), 1569-1573.
  • Lewin M. , On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc. 18 (1967) 63-68.
  • Netanyahu E., The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in |z|<1, Arch. Rational Mech. Anal. 32 (1969) 100-112.
  • Salagean G.S., Subclasses of univalent functions, Lecture Notes in Math., Springer, Berlin, 1013, 362-372, 1983.
  • Srivastava H. M., Bulut S., Çağlar M., and Yağmur N., a Coefficient estimates for a general subclass of analytic and biunivalent functions, a Filomat, vol. 27, no. 5, pp.831-842, 2013.
  • Srivastava H.M., Mishra A.K. and Gochhayat P., Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010) 1188-1192.
  • Srivastava H.M. , Sümer Eker S. , Ali RM., Coefficient bounds for a certain class of analytic and bi-univalent functions. Filomat 29 (2015) 1839-1845.
  • Taha T.S., Topics in Univalent Function Theory, Ph.D. Thesis, University of London, 1981.
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Bilal Seker Bu kişi benim

Veysi Mehmetoglu Bu kişi benim

Yayımlanma Tarihi 30 Eylül 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 4 Sayı: 3

Kaynak Göster

APA Seker, B., & Mehmetoglu, V. (2016). Coefficient bounds for new subclasses of bi-univalent functions. New Trends in Mathematical Sciences, 4(3), 197-203.
AMA Seker B, Mehmetoglu V. Coefficient bounds for new subclasses of bi-univalent functions. New Trends in Mathematical Sciences. Eylül 2016;4(3):197-203.
Chicago Seker, Bilal, ve Veysi Mehmetoglu. “Coefficient Bounds for New Subclasses of Bi-Univalent Functions”. New Trends in Mathematical Sciences 4, sy. 3 (Eylül 2016): 197-203.
EndNote Seker B, Mehmetoglu V (01 Eylül 2016) Coefficient bounds for new subclasses of bi-univalent functions. New Trends in Mathematical Sciences 4 3 197–203.
IEEE B. Seker ve V. Mehmetoglu, “Coefficient bounds for new subclasses of bi-univalent functions”, New Trends in Mathematical Sciences, c. 4, sy. 3, ss. 197–203, 2016.
ISNAD Seker, Bilal - Mehmetoglu, Veysi. “Coefficient Bounds for New Subclasses of Bi-Univalent Functions”. New Trends in Mathematical Sciences 4/3 (Eylül 2016), 197-203.
JAMA Seker B, Mehmetoglu V. Coefficient bounds for new subclasses of bi-univalent functions. New Trends in Mathematical Sciences. 2016;4:197–203.
MLA Seker, Bilal ve Veysi Mehmetoglu. “Coefficient Bounds for New Subclasses of Bi-Univalent Functions”. New Trends in Mathematical Sciences, c. 4, sy. 3, 2016, ss. 197-03.
Vancouver Seker B, Mehmetoglu V. Coefficient bounds for new subclasses of bi-univalent functions. New Trends in Mathematical Sciences. 2016;4(3):197-203.