Differential operator of meromorphic p-valent functions

Article Sidebar

PDF
Published: Sep 30, 2012
DOI: https://doi.org/10.5556/j.tkjm.43.2012.888
Keywords:
Analytic functions Meromorphic p-valent functions.

Main Article Content

Basem Aref Frasin
Faculty of Science, Department ofMathematics, Al al-Bayt University, P.O. Box: 130095 Mafraq, Jordan.

Abstract

A certain differential operator $ I_{λ}^{m}f(z) $ is introduced for functions of the form $f(z)=(1/(z^{p}))+∑_{n=k}^{∞}a_{n+p-1}z^{n+p-1} $  which are $p$-valent in the punctured unit disk $U^{∗}=\{z:z∈C \text{ and }  0<|z|<1\},$  where $p$  and $ k $ are positive integers. The main object of this paper is to give an application of the operator $I_{λ}^{m}f(z)$  to the differential inequalities.

Article Details

How to Cite
Frasin, B. A. (2012). Differential operator of meromorphic p-valent functions. Tamkang Journal of Mathematics, 43(3), 417–422. https://doi.org/10.5556/j.tkjm.43.2012.888
Issue
Vol. 43 No. 3 (2012)
Section
Papers
Author Biography

Basem Aref Frasin, Faculty of Science, Department ofMathematics, Al al-Bayt University, P.O. Box: 130095 Mafraq, Jordan.

Faculty of Science, Department ofMathematics, Al al-Bayt University, P.O. Box: 130095 Mafraq, Jordan.

References

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

B. A. Frasin and M. Darus, On certain meromorphic functions with positive coefficients, South East Asian Bulletin of Math., 28(2004), 615--623.

M. Kamali, On certain meromorphic p-valent starlike functions, J. Franklin Institute, 344, Issue 6,(2007), 867--872.

J. Liu and S. Owa,On certain meromorphic p-valent functions, Taiwanese J. Math., 2, (1)(1998), 107--110.

S. S. Miller and P. T. Mocanu, Second order differential inequalities in the complex plane, J. Math. Anal. Appl., 65(1978), 289--305.

S. Ruscheweyh, New criteria for univalent functions, Proc. Amer. Math. Soc., 49 (1975), 109--115.

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