Certain classes of analytic functions with varying arguments
For the subclasses \({\mathcal B}_{\alpha}\) and \({\mathcal C}_{\alpha}\) of analytic functions satisfying \[ Re\{f(z)/z\}>\alpha \quad (0\leq \alpha <1)\quad and\quad Re\{f'(z)\}>\alpha \quad (0\leq \alpha <1), \] respectively, the authors prove various coefficient inequalities and distortion theorems, and determine the radius of convexity and starlikeness of such functions. They also consider an interesting application of the fractional calculus involving analytic functions belonging to these subclasses.
scientific article; zbMATH DE number 4048022
scientific article