The univalence conditions for a general integral operator (Q617000)

The authors investigate the univalence of the integral operator \[ \left( \eta\beta\int_0^z u^{\eta\beta-1} \prod\bigg(\frac{f_i(u)}{u}\bigg)^{1/\gamma_i} du\right)^{1/\eta\beta}, \] where the product is from \(i=1\) through \([|\eta|]\). With \(i\) varying from 1 through \(|\Re(\eta)|\) in the product, a similar work was earlier done by \textit{N. Breaz, V. Pescar} and \textit{D. Breaz} [Math. Comput. Modelling 52, No. 1--2, 241--246 (2010; Zbl 1201.30009)].