Lebesgue-Stieltjes integral inequalities in several variables with retardation
In the paper, using two known Lebesgue-Stieltjes integral inequalities by the same author [Chin. J. Math. 17, No.1, 29-50 (1989; Zbl 0676.26008)], five new nonlinear Lebesgue-Stieltjes integral inequalities of Gronwall type in several variables with retardation are obtained. These results generalize and unify some continuous and discrete inequalities established by \textit{O. Akinyele} [J. Math. Anal. Appl. 104, 1-26 (1984; Zbl 0604.26011), Theorem 4], \textit{F. M. Dannan} [J. Math. Anal. Appl. 108, 151-164 (1985; Zbl 0586.26008), Theorems 1 and 2], \textit{C. C. Yeh} [J. Math. Anal. Appl. 105, 322-332 (1985; Zbl 0604.26012), Theorem 2], and \textit{S. M. Singare} and \textit{G. B. Pachpatte} [Pac. J. Math. 82, 197- 210 (1979; Zbl 0413.26009)]. Several misprints are in the article. In this reviewer's opinion some more steps are needed in the proof of Theorem 3.2. Because the first term on the right-hand side of the nonlinear inequality on page 236 (line 2 to 4) is not a nonnegative constant as required by the Lemma 2.2.
Lebesgue-Stieltjes integral inequalities of Gronwall type in several variables
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