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The abstract renewal equation. (English) Zbl 0968.45006
Summary: The abstract Perron-Stieltjes integral defined in the Kurzweil-Henstock sense is used for introducing Stieltjes convolutions. The approach is used for obtaining basic existence result for the abstract renewal equation which was studied e. g. by O. Diekmann, M. Gyllenberg and H. R. Thieme [Differ. Integral Equ. 6, No. 1, 155-181 (1993; Zbl 0770.47012); ibid. 8, No. 5, 1205-1244 (1995; Zbl 0834.47043)].
##### MSC:
 45N05 Abstract integral equations, integral equations in abstract spaces 92D25 Population dynamics (general)
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