Double subordination preserving properties for a new generalized Srivastava-Attiya integral operator
Let \(\mathcal A\) be the class of analytic functions \(f\) in the unit disk \(U\) of the form \(f(z)=z+\sum_{n=2}^\infty a_nz^n\), and, for \(\lambda,\mu,s\in\mathbb C\) and \(\nu, a\in\mathbb C\setminus\mathbb Z^-\), let \(\mathcal J_{\lambda,\mu;\nu}^{s,a}:\mathcal A\to\mathcal A\) be the linear operator defined by \[ \mathcal J_{\lambda,\mu;\nu}^{s,a}f(z)=z+\sum_{n=2}^\infty\frac{(\lambda+1)_{n-1}(\mu+1)_{n-1}}{(\nu+1)_{n-1}n!}\left(\frac{1+a}{n+a}\right)^sa_nz^n, \;z\in U. \] This operator, named by the authors the ``Srivastava-Attiya operator'', is the object of the paper. Two results concerning subordination and superordination with such kind of operators are given, and a lot of consequences are also found, some of them involving generalized hypergeometric functions.
scientific article; zbMATH DE number 6112849
scientific article