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• W2070758142 abstract "In the real case, these theorems give sufficient conditions for the validity of the inequality yl(x) _y2(x), where yi is the unique solution of (1.1). These theorems are simple consequences of well-known facts concerning integral equations of the form (1.1). These facts are briefly summarized in ?2; the reader is referred to [3] and [4] for the details. As in [3], [4] we deal with Lebesgue square integrable functions throughout so that all equalities (and inequalities) are of the almost everywhere kind. In this section, we also give an upper bound for yi(x)I in (1.1). The last section of this paper deals with integral inequalities related to Volterra integral equations of the second kind. These results are closely related to the positivity of the operator L(y) =y -Ky, and include an extension to the L2 case of the recent theorem of Chu and Metcalfe [5]. As pointed out in [5] this theorem includes the classical Gronwall inequality and some of its linear extensions. It should also be noted that it was pointed out by Bellman in [6] that such inequalities are closely related to the positivity of operators." @default.
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• W2070758142 date "1969-01-01" @default.
• W2070758142 modified "2023-09-26" @default.
• W2070758142 title "Comparison theorems and integral inequalities for Volterra integral equations" @default.
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• W2070758142 doi "https://doi.org/10.1090/s0002-9939-1969-0234228-3" @default.
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