ON A CERTAIN CONVOLUTION OPERATOR FOR MEROMORPHIC FUNCTIONS
DOI:
https://doi.org/10.5556/j.tkjm.25.1994.4444Keywords:
Convolution operator, meromophic functionsAbstract
A certain convolution operator $D^\alpha f(z)$ for meromorphic functions and two subclasses $M(\alpha)$ and $J(\alpha)$ are introduced. The object of the present paper is to derive some properties of the classes $M(\alpha)$ and $J(\alpha)$. The results of the paper are the generalizations and the improvements of the former results.
References
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J I.S. Jack, "Functions starlike and convex of order alpha," J. London Math. Soc. (2)3(1971), 469-474.
S. S. Miller and P. T. Mocanu,"Second order differential inequalities in the complex plane," J. Math. Anal. Appl. 65(1978), 289-305.
B.A. Uralegaddi and M.D. Ganigi, "A new criterion for meromorphic convex functions," Tamkang J. Math. 19(1988), 43-48.
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