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Weighted Favard and Berwald inequalities. (English) Zbl 0834.26012

Generalizations of inequalities by J. Favard [Bull. Sci. Math., II. Ser. 57, 54-64 (1933; Zbl 0007.06104)] and L. Berwald [Acta Math. 79, 17-37 (1947; Zbl 0029.11704)] and related inequalities are offered for the case with weight functions in the integrals compared. The statements and proofs are highly technical.

MSC:

26D15 Inequalities for sums, series and integrals
26A51 Convexity of real functions in one variable, generalizations
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