Characterization properties for starlike and convex functions involving a class of fractional integral operators
Let \(T_n\) denote the class of functions \(f(z)=z+ \sum^\infty_{k=n+1} a_kz^k\) which are analytic in the unit disc \(U\) and let \(S^*_n\) and \(K_n\) denote the functions \(f\in T_n\) which are, respectively, starlike and convex in \(U\). Using a generalization of the Erdélyi-Kober fractional integral operators in which the \(H\)-function of Fox appears in the kernel, introduced by \textit{V. Kiryakova} [Mat. Vesn. 40, No. 3/4, 259-266 (1988; Zbl 0713.33006)], the authors define a new class of fractional integral operators. In this paper, characterization properties satisfied by this operators of certain analytic functions in \(U\) to be in \(S^*_n\) and \(K_n\) are studied. Characterization theorems associated with the Hadamard product are also proved.
scientific article; zbMATH DE number 1089770
scientific article