ANALYTICAL AND GEOMETRICAL PROPERTIES OF NEW CLASS OF UNIVALENT FUNCTIONS ASSOCIATED WITH THE FRACTIONAL DERIVATIVE OPERATOR
ANALYTICAL AND GEOMETRICAL PROPERTIES OF NEW CLASS OF UNIVALENT FUNCTIONS
Abstract
In this work, we introduce and analyze a new subclass $\mathcal{F}_{0,z}^\varrho(\varepsilon, \lambda,\eta,\mu)$ of analytic univalent functions related to the fractional derivative operator within the open unit disk
$ \mathbb{U}=\{z:z\in \mathbb{C},|z|<1\}$. We investigate coefficient estimates, distortion bounds and growth theorems, convex set, radius of convexity, radius of stralikeness, arithmetic mean, weighted mean, and also we establish some basic results like extreme points, Hadamard product, closure theorem for the functions in the class.
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