A CRITICAL STUDY OF MEROMORPHIC STARLIKE FUNCTIONS

Abstract

An attempt has been made to introduce a new criterion to make it possible to change meromorphic analytic function into a meromorphic starlike function of particular order. This criterion is based on a dierential operator which is dened in a punctured unit disk U. By using this criterion, one can nd easily dierent types of meromorphic starlike functions of specic order.

Keywords

• Meromorphic functions,meromorphic starlike functions,dierential operators.

References

1. Royster, W. C., (1963), Meromorphic starlike multivalent functions, Trans. Amer. Math. Soc., 107, pp. 300-308.
2. El-Ashwah, R. M., (2009), A note on certain meromorphic p-valent functions, App. Math. Lett., 22, pp. 1756-1759.
3. Cho, N. E., Kwon, O. S. and Srivastava, H. M., (2004), Inclusion and argument propertie for certain subclasses of meromorphic functions associated with a family of multiplier transformations, J. Math. Anal. Appl., 300, pp. 505-520.
4. Cho, N. E., Kwon, O. S. and Srivastava, H. M., (2005), Inclusion relationships for certain subclasses of meromorphic functions associted with a family of multiplier transformations, Integral Transforms
5. Special Functions, 16 (18), pp. 647-659. Aouf, M. K. and Hossen, H. M., (1993), New criteria for meromorphic p-valent starlike functions, Tsukuba J. Math., 17, pp. 481-486.
6. Liu, J. L. and Owa, S., (1998), On certain meromorphic p-valent functions, Taiwanese J. Math., 2 (1), pp. 107-110.
7. Liu, J. L. and Srivastava, H. M., (2004), Subclasses of meromorphicaly multivalent functions associated with certain linear operator, Math. Comput. Mode., 39 (1), pp. 35-44.
8. Srivastava, H. M. and Patel, J., (2005), Applications of differential subordination to certain classes of meromorphicaly multivalent functions, J. Ineq. Pure Appl. Math., 6 (3), Art. 88, pp. 15.

9. Uralegaddi, B. A. and Somanatha, C., (1991), New criteria for meromorphic starlike univalent func- tions, Bull. Austral. Math. Soc., 43, pp. 137-140.
10. El-Ashwah, R. M. and Aouf, M. K., (2010), Differential subordination and superordination on p-valent meromorphic functions defined by extended multiplier transformations, European J. Pure Appl. Math., (3), pp. 1070-1085.
11. Duren, P. L., (1983), Univalent functions, Grundlehren der Mathematischen Wissenschaften, Band , Springer-Verlag, New York.
12. Srivastava, H. M. and Owa, S., (Eds.), (1992), Current topics in analytic function theory, World
13. Scientific, Singapore. Srivastava, H. M. and Owa, S., (1987), Some characterization and distortion theorems involving fractional calculus, generalized hypergeometric functions, hadamard products, linear operators, and certain subclasses of analytic functions, Nagoya Math. J., 106, pp. 1-28.
14. Cho, N. E., Kwon, O. S. and Srivastava, H. M., (2003), Inclusion and argument properties for certain subclasses of meromorphic functions associated with a family of multiplier transformations, J. Math. Anal. Appl., 286, pp. 168-176.
15. Ruscheweyh, S., (1975), New criteria for univalent functions, Proc. Amer. Math. Soc., 49, pp. 109-115.
16. Liu, J. L., (1996), Note on Ruscheweyh derivatives, J. Math. Anal. Appl., 199, pp. 936-940.
17. Lee, S. K. and Joshi, S. B., (1999), A certain class of analytic functions defined by ruscheweyh derivatives, Comm. Korean Math. Soc., 14, pp. 234-237.
18. Al-Amiri, H. S., (1980), On Ruscheweyh derivatives, Ann. Polon. Math., 38 pp. 87-94.
19. Sun, Y., Kuang, W. P. and Wang, Z. G., (2012), On meromorphic starlike functions of reciprocal order α, Bull. Malays. Math. Sci. Soc., 35, pp. 469-477.
20. Erdelyi, A., (1956), Asymptotic expansions, Dover publications, New York.