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Partial Sums for Certain Subclasses of Meromorphically Univalent Functions

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Abstract (2. Language): 
In this paper we introduce and study a subclass M,k P ( , ) of meromorphically univalent functions defined by generalized Liu-Srivastava operator. We obtain coefficient estimates, extreme points, growth and distortion bounds, radii of meromorphic starlikeness and meromorphic convexity for the classM,k P ( , ) by fixing the second coefficient. Further, it is shown that the classM,k P ( , ) is closed under convex linear combination.
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REFERENCES

References: 

[1] R. Aghalary, Some properties of a certain family of meromorphically univalent functions
defined by an integral operator, Kyungpook Math. J. 48, no. 3, 379–385. 2008.
[2] O. Altınta¸s, H. Irmak and H. M. Srivastava, A family of meromorphically univalent functions
with positive coefficients, Panamer. Math. J. 5, no. 1, 75–81. 1995.
[3] M. K. Aouf, A certain subclass of meromorphically starlike functions with positive coefficients,
Rend. Mat. Appl. (7) 9, no. 2, 225–235. 1989.
[4] M. K. Aouf, On a certain class of meromorphic univalent functions with positive coefficients,
Rend. Mat. Appl. (7) 11, no. 2, 209–219. 1991.
[5] M. K. Aouf and H. E. Darwish, Certain meromorphically starlike functions with positive
and fixed second coefficients, Turkish J. Math. 21, no. 3, 311–316. 1997.
[6] M. K. Aouf and S. B. Joshi, On certain subclasses of meromorphically starlike functions
with positive coefficients, Soochow J. Math. 24, no. 2, 79–90. 1998.
[7] N. E. Cho and S. Owa, Partial sums of certain meromorphic functions, JIPAM. J. Inequal.
Pure Appl. Math. 5, no. 2, Article 30, pp. 7. 2004.
[8] N. E. Cho and I. H. Kim, Inclusion properties of certain classes of meromorphic functions
associated with the generalized hypergeometric function, Appl. Math. Comput. 187,
no. 1, 115–121. 2007.
[9] J. Dziok and H. M. Srivastava, Classes of analytic functions associated with the generalized
hypergeometric function, Appl. Math. Comput. 103, no. 1, 1–13. 1999
[10] M. R. Ganigi and B. A. Uralegaddi, New criteria for meromorphic univalent functions,
Bull. Math. Soc. Sci. Math. R. S. Roumanie (N.S.) 33(81), no. 1, 9–13. 1989.
REFERENCES 99
[11] F. Ghanim and M. Darus, On class of hypergeometric meromorphic functions with fixed
second positive coefficients, Gen. Math. 17, no. 4, 13–28. 2009.
[12] S. Hussain, A new class of meromorphic functions, Acta Universitatis Apulensis, 24,
181–187. 2010.
[13] S. R. Kulkarni and S. S. S. Joshi, On a subclass of meromorphic univalent functions with
positive coefficients, J. Indian Acad. Math. 24, no. 1, 197–205. 2002.
[14] S. Latha and L. Shivarudrappa, Partial sums of some meromorphic functions, JIPAM. J.
Inequal. Pure Appl. Math. 7, no. 4, Article 140, pp. 8. 2006.
[15] J.-L. Liu and H. M. Srivastava, A linear operator and associated families of meromorphically
multivalent functions, J. Math. Anal. Appl. 259, no. 2, 566–581. 2001.
[16] J.-L. Liu and H. M. Srivastava, Classes of meromorphically multivalent functions associated
with the generalized hypergeometric function, Math. Comput. Modelling 39, no. 1,
21–34. 2004.
[17] J.-L. Liu and H. M. Srivastava, Subclasses of meromorphically multivalent functions
associated with a certain linear operator, Math. Comput. Modelling 39, no. 1, 35–44.
2004.
[18] M. L. Mogra, T. R. Reddy and O. P. Juneja, Meromorphic univalent functions with positive
coefficients, Bull. Austral. Math. Soc. 32, no. 2, 161–176. 1985.
[19] H. Silverman, Partial sums of starlike and convex functions, J. Math. Anal. Appl. 209,
no. 1, 221–227. 1997.
[20] B. A. Uralegaddi, Meromorphically starlike functions with positive and fixed second
coefficients, Kyungpook Math. J. 29, no. 1, 64–68. 1989.
[21] D. Yang, On a class of meromorphic starlike multivalent functions, Bull. Inst. Math.
Acad. Sinica 24, no. 2, 151–157. 1996.
[22] D. Yang, Certain convolution operators for meromorphic functions, Southeast Asian Bull.
Math. 25, no. 1, 175–186. 2001.

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