A class of functions defined by using Hadamard product
We introduce a class \({\mathbb{P}}_{\alpha}[\beta,\gamma]\) of functions defined by using Hadamard product \(f*S_{\alpha}(z)\) of f(z) and \(S_{\alpha}(z)=z/(1-z)^{2(1-\alpha)}\). The object of the present paper is to determine extreme points, coefficient inequalities, distortion theorems, and radii of starlikeness and convexity for functions in \({\mathbb{P}}_{\alpha}[\beta,\gamma]\). Further, we give distortion theorems for fractional calculus of functions belonging to the class \({\mathbb{P}}_{\alpha}[\beta,\gamma]\).
scientific article; zbMATH DE number 3989712