Fractional calculus and some properties of certain starlike functions with negative coefficients. (Q1856031)

Let \(T(n,p)\) denote the class of functions of the form \[ f(z)= z^p- \sum^\infty_{k=n} a_{k+p} z^{k+p} \] (\(a_{k+p}\geq 0\); \(p\in \{1,2,\dots\}\), \(n\in\mathbb{N}\)) analytic in the open unit disk \(U\). The authors introduce the class \(T_\gamma(n,p,\lambda,\alpha)\), a general subclass of \(T(n,p)\). Coefficient bounds and results concerning the Hadamard product for this functions are given. Several distortion theorems involving operators of fractional calculus defined e.g. in \textit{S. Owa} [Kyungpook Math. J. 18, 53--59 (1978; Zbl 0401.30009)] are proved.