Convex subclass of starlike functions (Q2718043)

Let \(T\) denote the class of functions of the form \(f(z) = z-\sum^\infty_{n=2} a_nz^n\) \((a_n\geq 0)\) that are analytic and univalent in the unit disc \(U\). In this paper the authors obtain a relationship between the subclasses \(T(\lambda,\alpha)\) and \(K(\lambda,\alpha)\) of \(T\) by defining a subclass \(B(\lambda,\alpha)\) of \(K(\lambda,\alpha)\). Coefficient estimate, distortion and covering theorems are obtained for the class \(B(\lambda,\alpha)\). The class \(B(\lambda,\alpha)\) is convex. In terms of the operators of fractional calculus derive several sharp results depicting the growth and distortion properties of functions belonging to the class \(B(\lambda,\alpha)\).