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

Year 2014, Volume: 4 Issue: 1, 39 - 44, 01.06.2014

Abstract

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.

References

  • 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.
Year 2014, Volume: 4 Issue: 1, 39 - 44, 01.06.2014

Abstract

References

  • 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.
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Details

Primary Language English
Journal Section Research Article
Authors

Fateh S. Aziz This is me

Abdul Rahman S. Juma This is me

Publication Date June 1, 2014
Published in Issue Year 2014 Volume: 4 Issue: 1

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