Some Families of Multivalently Analytic Functions with Negative Coefficients

Abstract

The authors introduce and study three novel subclasses of analytic and p-valent functions with negative coefficients. In addition to finding a necessary and sufficient condition for a function to belong to each of these subclasses, a number of other potentially useful properties and characteristics of functions in these subclasses are obtained. Finally, several applications involving an integral operator and certain fractional calculus operators are also considered. ᮊ 1997 Academic Press *

Certain Operators and Inequalities and Their Applications to Meromorphically Multivalent Functions

“…We define w(z) by (7), so that |w(z)| < 1 (z 6 U). Thus, definition (8) immediately yields the inequality (1), that is f(z) e W p (m, q\ a). Hence, the proof is completed.…”

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