The paper considers one of the possible generalizations of the Volterra equations in the case when the independent variable belongs to an arbitrary compact metric space and, as a corollary of the obtained results, an abstract analog of the Bellman-Gronwall inequality is proved.
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D. D. Bainov, A. D. Myshkis, A. I. Zahariev, On an Abstract Analog of the Bellmann-Gronwall Inequality. Publ. Res. Inst. Math. Sci. 20 (1984), no. 5, pp. 903–911DOI 10.2977/PRIMS/1195180871