On certain classes of meromorphically p-valent starlike and p-valent quasi-convex functions

Main Article Content

Janusz Sokol
Jacek Dziok
M. K. Aouf

Abstract

By making use of a familiar analogue of the generalized hypergeometric function, we introduce and investigate some inclusion properties of certain class of meromorphically p-valent starlike functions of order $\lambda \ $ and certain class of meromorphically p-valent quasi-convex functions of order $\lambda $.

Article Details

How to Cite
Sokol, J., Dziok, J., & Aouf, M. K. (2013). On certain classes of meromorphically p-valent starlike and p-valent quasi-convex functions. Tamkang Journal of Mathematics, 44(3), 271–278. https://doi.org/10.5556/j.tkjm.44.2013.1030
Section
Papers
Author Biographies

Janusz Sokol

Department ofMathematics, Rzeszów University of Technology, ul. W. Pola 2, 35-959 Rzeszów, Poland.

Jacek Dziok

Institue ofMathematics, University of Rzeszów, ul. Rejtana 16A, 35-310 Rzeszów, Poland.

M. K. Aouf

Department ofMathematics, Faculty of Science,Mansoura University,Mansoura 35516, Egypt.

References

M. K. Aouf, New criteria for multivalent meromorphic functions of order alpha, Proc. Japan Acad., 69 Ser. A(1993), 66--70.

M. K. Aouf, Certain subclasses of meromorphically multivalent functions associated with generalized hypergeometric function, Comput. Math. Appl., 55(2008), 494--509.

M. K. Aouf and H. M. Srivastava, A new criterion for meromorphically p-valent convex functions of order alpha, Math. Sci. Res. Hot-Line, (1997), no. 8, 7--12.

S. K. Bajpai, A note on a class of meromorphic univalent functions, Rev. Roum. Math. Pures Appl., 22(1972), 295--297.

N. E. Cho, Some new criteria for meromorphicaaly p-valent starlike functions, in: H. M. Srivastava and S. Owa (Eds.), Current Topics in Analytic Function Theory, World Scientific Publishing Company, Singapore, New Jersey, London and Hong Kong, 1992, 86--93.

N. E. Cho and S. Owa, On certain classes of meromorphically p-valent starlike functions, in H. M. Srivastava and S. Owa (Eds.), Current Topics in Analytic Function Theory, World Scientific Publishing Company, Singapore, New Jersey, London and Hong Kong, 1992, 159--165.

J. Dziok, H. M. Srivastava, Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput., 103 (1999), 1--13

J. Dziok, H. M. Srivastava, Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transform. Spec. Funct., 14 (2003), 7--18.

R. M. Goel and N. S. Sohi, On a class of meromorphic functions, Glas. Mat.,17(1981), 19--28.

I. S. Jack, Functions starlike and convex of order $alpha $, London Math. Soc.,2(1971),469--474.

S. R. Kulkarni, U. H. Naik and H. M. Srivastava, A certain class of meromorphically p-valent quasi-convex functions, PanAmer. Math. J., 8(1998), 57--64.

J. -L. Liu and H. M. Srivatava, A linear operator and associated families of meromorphically multivalent functions, J. Math. Anal. Appl., 259(2000), 566--581.

J. -L. Liu and H. M. Srivastava, Classes of meromorphically multivalent functions with the generalized hypergeometric function, Math. Comput. Modelling, 39(2004), 21--34.

T. H. MacGregor, Radius of univalence of certain analytic functions, Proc. Amer. Math. Soc., 14(1963), 514--520.

H. M. Srivastava and P. W. Karlsson, Multiple Gaussion Hypergeometric Series, Halsted Press, Ellis Horwood Limited, Chichester, John Wiley and Sons, New York, Chichester, Brisbane, Toronto, 1985.

B. A. Uralegaddi and C. Somanatha, Certain classes of meromorphic multivalent functions, Tamkang J. Math., 23(1992), 223--231.