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Difference between weighted integral means

Cerone P.

Demonstratio Mathematica

2002

Vol. 35, nr 2

251-265

Weighted integral means over [c, d] and [a, b] where [c, d] C [a, 6] are compared in the current work by determining bounds for their difference in terms of a variety of norms. The bounds are obtained and involve the behaviour of at most the first derivative. Previous work for unweighted integral means is recaptured as particular cases if the weights are taken to be unity. By a limiting shrinking of the subinterval [c, d] to a single point, weighted Ostrowski type inequalities are shown to be recaptured, under certain conditions as particular instances of the current development.