Subordination and superordination of certain linear operator on meromorphic functions

M. K. Aouf, T. M. Seoudy

Abstract


Using the methods of differential subordination and superordination, sufficient conditions are determined on the differential linear operator of meromorphic functions in the punctured unit disk to obtain, respectively, the best dominant and the best subordinant. New sandwich-type results are also obtained.

Keywords


Analytic function; linear operator; Hadamard product; differential subordination; superordination

Full Text:

PDF

References


Ali, R. M., Ravichandran, V. and Seenivasagan, N., Subordination and superordination of Liu-Srivastava linear operator on meromorphic functions, Bull. Malays. Math. Sci. Soc. 31, no. 2 (2008), 193-207.

Aouf, M. K., Hossen, H. M., New criteria for meromorphic p-valent starlike functions, Tsukuba J. Math. 17 (1993), 481-486.

Liu, J.-L., Owa, S., Certain meromorphic p-valent functions, Taiwanese J. Math. 2, no. 1 (1998), 107-110.

Liu, J.-L., Srivastava, H. M., Subclasses of meromorphically multivalent functions associated with a certain linear operator, Math. Comput. Modelling 39, no. 1 (2004), 35-44.

Miller, S. S, Mocanu, P. T., Differential Subordinations: Theory and Applications, Series on Monographs and Textbooks in Pure and Applied Mathematics, Vol. 225, Marcel Dekker, New York and Basel, 2000.

Miller, S. S, Mocanu, P. T., Subordinants of differential superordinations, Complex Var. Theory Appl. 48, no. 10 (2003), 815-826.

Srivastava, H. M., Patel, J., Applications of differential subordinations to certain classes of meromorphically multivalent functions, J. Ineq. Pure Appl. Math. 6, no. 3, art. 88 (2005), pp. 15.

Uralegaddi, B. A., Somanatha, C., New criteria for meromorphic starlike univalent functions, Bull. Austral. Math. Soc. 43 (1991), 137-140.




DOI: http://dx.doi.org/10.17951/a.2010.54.1.1-16
Data publikacji: 2016-07-29 22:06:15
Data złożenia artykułu: 2016-07-29 17:30:03

Refbacks

  • There are currently no refbacks.


Copyright (c) 2010 M. K. Aouf, T. M. Seoudy