Convolution and Differential Subordination for Multivalent Functions
نویسندگان
چکیده
The general classes of multivalent starlike, convex, close-to-convex and quasiconvex functions are introduced. These classes provide a unified treatment to various known subclasses. Inclusion and convolution properties are derived using the methods of convex hull and differential subordination. 1. Motivation and Preliminaries Let U = {z : |z| < 1} be the unit disk and H(U) be the class of all analytic functions defined on U . Let Ap be the class of all analytic functions of the form f(z) = zp + ap+1z + . . . with A := A1. For two functions f(z) = z+ap+1z + . . . and g(z) = zp+ bp+1z + . . . in Ap, the Hadamard product (or convolution) of f and g is the function f ∗ g defined by (f ∗ g)(z) = z + ∞ ∑
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