Certain inequalities for the Kampé de Fériet function (Q1095286)

The authors obtain some two-sided inequalities by applying fractional derivatives to certain known inequalities of \textit{Y. L. Luke} [J. Approximation theory 11, 73-84 (1974; Zbl 0276.33009)]. One of the results given in the paper is \[ F_ 1(\alpha,1,\beta;\gamma;-\lambda \theta z,yz)\quad <\quad F_{1;p;0}^{1;p+1;1}\left[ \begin{matrix} \alpha;\lambda,(g_ p);\beta;\\ \gamma;(h_ p);...;\end{matrix} -z,yz\right] \] \[ <(1-\frac{2\lambda \theta}{(\lambda +1)\phi})_ 2F_ 1(\beta,\alpha;\gamma;yz)+\frac{2\lambda \theta}{(\lambda +1)\phi}\times F_ 1(\alpha,1,\beta;\gamma;(\frac{\lambda +1)}{2})\phi z,yz), \] where \(0<z<1\), \(0<y<1\), \(\gamma \geq \alpha >0\), \(h_ j\geq g_ j>0\) (j- 1,...,p), \[ \theta =\prod^{p}_{j=1}(g_ j)/(h_ j),\quad and\quad \phi =\prod^{p}_{j=1}(g_ j+1)/(h_ j+1). \] The method of derivation adopted by the authors was given much earlier by the reviewer [Math. Stud. 46(1982), 165-171 (1978; Zbl 0531.33012)]. The present work of the author is in this direction. It, however (perhaps inadvertently), misses a mention of the reviewer's paper.