Abstract
In this article, the operator inequalities and with linear positive operator K are analyzed in a real Banach space. The obtained results are applied to linear Fredholm and Volterra integral inequalities of the second kind with general continuous nonnegative kernel k(x, s). These results are all new. For a special case of a Volterra inequality, Gronwall’s lemma is deduced, however, in a manner that is different from the known one. The general results may also be applied to Fredholm-type and Volterra-type matrix inequalities.
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