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ESTIMATING COEFFICIENTS FOR SUBCLASSES OF MEROMORPHIC BI-UNIVALENT FUNCTIONS ASSOCIATED WITH LINEAR OPERATOR

Yıl 2014, Cilt: 4 Sayı: 1, 39 - 44, 01.06.2014

Öz

In this paper we define a differential linear operator, applying it on the subclasses HΣ∗B α, n, λ of meromorphic starlike bi-univalent functions of order α, and HΣ˜ ∗B α, n, λ of meromorphic strongly starlike bi-univalent functions of order α, also we find estimates on the coefficients |bo| and |b1| for functions in these subclasses.

Kaynakça

  • Juma A.S. and Aziz F.S., (2012), Applying Ruscheweyh derivative on two sub-classes of bi-univalent functions, Inter. J. of Basic & Appl. Sci., V.,12 no.,06 , pp. 68-74.
  • Ali R.M., Lee S.K., Ravichandran V., Supramaniam S., Coefficient estimates for bi-univalent Ma- Minda starlike and convex functions, preprint. Brannan D.A. and Clunie J.G., (1980), Aspects of contemporary complex analysis, (Proceedings of the NATO Advanced Study Instituteheld at the university of Durham, Durham,July 12, 1979), Academic
  • Press, London and New York. Brannan D.A. and Taha T.S., (1986), On some classesof bi-univalent functions, Studia Univ. Babes- Bolyai Math. 31, no. 2, pp. 70-77.
  • Duren P.L., (1983), Univalent functions, in: Grunddlehren der mathematischen Wissenschaften, Band , Springer -Verlag, New York, Berlin, Hidelberg and Tokyo, .
  • Duren P.L., (1971), Coefficients of meromorphic schlicht functions, Proc. Amer. Math. Soc., 28, pp. 172.
  • Frasin B.A., Aouf M.K., (2011) New subclasses of bi-univalent functions, Appl. Math. Lett., 24 (9) pp.1569-1573.
  • Goodman A.W., (1983) Univalent functions, Vol. 1, Polygonal Puplishing House, Washington, New Jersey.
  • Kapoor G.P. and Mishra A.K., (2007), Coefficient estimates for inverses of starlike functions of positive order, J. Math. Anal. Appl., 329 , no. 2, pp. 922-934.
  • Kubota Y., (1976-77), Coefficientsof meromorphic univalent functions, K¯odai Math. Sem. Rep., 28, no. 2-3, pp. 253-261.
  • Lewin M., (1967), On a coefficient problem for bi-univalent functions, Proc. Amer.Math. Soc. 18, pp. 68.
  • Netanyahu E., (1969), 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 , pp. 100-112.
  • Schiffer M., (1938), Sur un probl`eme d’extr´emum de la repr´esentation conforme, Bull. Soc. Math. France, 66 ,pp. 48-55.
  • Schober G., (1977), Coefficients of inverses of meromorphic univalent functions, Proc. Amer. Math. Soc., 67 ,no. 1, pp. 111-116.
  • Springer G., (1951), The coefficient problem for schlicht mappings of the exterior of the unit circle
  • Trans. Amer. Math. Soc., 70 , pp. 421-450. Srivastava H.M., Mishra A.K., Gochhayat P., (2010), Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., 23, no. 10, pp. 1188-1192.
Yıl 2014, Cilt: 4 Sayı: 1, 39 - 44, 01.06.2014

Öz

Kaynakça

  • Juma A.S. and Aziz F.S., (2012), Applying Ruscheweyh derivative on two sub-classes of bi-univalent functions, Inter. J. of Basic & Appl. Sci., V.,12 no.,06 , pp. 68-74.
  • Ali R.M., Lee S.K., Ravichandran V., Supramaniam S., Coefficient estimates for bi-univalent Ma- Minda starlike and convex functions, preprint. Brannan D.A. and Clunie J.G., (1980), Aspects of contemporary complex analysis, (Proceedings of the NATO Advanced Study Instituteheld at the university of Durham, Durham,July 12, 1979), Academic
  • Press, London and New York. Brannan D.A. and Taha T.S., (1986), On some classesof bi-univalent functions, Studia Univ. Babes- Bolyai Math. 31, no. 2, pp. 70-77.
  • Duren P.L., (1983), Univalent functions, in: Grunddlehren der mathematischen Wissenschaften, Band , Springer -Verlag, New York, Berlin, Hidelberg and Tokyo, .
  • Duren P.L., (1971), Coefficients of meromorphic schlicht functions, Proc. Amer. Math. Soc., 28, pp. 172.
  • Frasin B.A., Aouf M.K., (2011) New subclasses of bi-univalent functions, Appl. Math. Lett., 24 (9) pp.1569-1573.
  • Goodman A.W., (1983) Univalent functions, Vol. 1, Polygonal Puplishing House, Washington, New Jersey.
  • Kapoor G.P. and Mishra A.K., (2007), Coefficient estimates for inverses of starlike functions of positive order, J. Math. Anal. Appl., 329 , no. 2, pp. 922-934.
  • Kubota Y., (1976-77), Coefficientsof meromorphic univalent functions, K¯odai Math. Sem. Rep., 28, no. 2-3, pp. 253-261.
  • Lewin M., (1967), On a coefficient problem for bi-univalent functions, Proc. Amer.Math. Soc. 18, pp. 68.
  • Netanyahu E., (1969), 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 , pp. 100-112.
  • Schiffer M., (1938), Sur un probl`eme d’extr´emum de la repr´esentation conforme, Bull. Soc. Math. France, 66 ,pp. 48-55.
  • Schober G., (1977), Coefficients of inverses of meromorphic univalent functions, Proc. Amer. Math. Soc., 67 ,no. 1, pp. 111-116.
  • Springer G., (1951), The coefficient problem for schlicht mappings of the exterior of the unit circle
  • Trans. Amer. Math. Soc., 70 , pp. 421-450. Srivastava H.M., Mishra A.K., Gochhayat P., (2010), Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., 23, no. 10, pp. 1188-1192.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

Fateh S. Aziz Bu kişi benim

Abdul Rahman S. Juma Bu kişi benim

Yayımlanma Tarihi 1 Haziran 2014
Yayımlandığı Sayı Yıl 2014 Cilt: 4 Sayı: 1

Kaynak Göster