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

Kirti Pal; Anokhe Lal Pathak; Lakshmi Narayan Mishra

doi:10.5269/bspm.79103

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

Autores/as

Kirti Pal Department of Mathematics, Brahmananad P.G. College, The Mall, Kanpur 208011, Uttar Pradesh, India
Anokhe Lal Pathak Department of Mathematics, Brahmananad P.G. College, The Mall, Kanpur 208011, Uttar Pradesh, India
Lakshmi Narayan Mishra Lovely Professional University, Jalandhar-Delhi G.T. Road, Phagwara, Punjab 144 411, India. http://orcid.org/0000-0001-7774-7290

DOI:

https://doi.org/10.5269/bspm.79103

Resumen

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.