Abstract
In this paper, we first prove an integral majorization theorem related to integral inequalities for functions defined on rectangles. We then apply the result to establish some new integral inequalities for functions defined on rectangles. The results obtained are generalizations of weighted Favard’s inequality, which also provide a generalization of the results given by Maligranda et al. (J. Math. Anal. Appl. 190:248–262, 1995) in an earlier paper.
Highlights
There is a certain intuitive appeal to the vague notion that the components of an n-tuple x are less spread out, or more nearly equal, than the components of an n-tuple y
A mathematical origin of majorization is illustrated by the work of
We extend majorization and Favard inequalities from functions defined on intervals to functions defined on rectangles
Summary
There is a certain intuitive appeal to the vague notion that the components of an n-tuple x are less spread out, or more nearly equal, than the components of an n-tuple y. The inequality asserted by Theorem 1.1 is called majorization inequality It is an inequality in elementary algebra for convex real-valued functions defined on an interval of the real line, and it generalizes the finite form of Jensen’s inequality. This majorization ordering is equivalently described in Kemperman’s review [25]. Have been used and generalized by majorization inequalities for n-convex functions; see [1,2,3,4,5,6,7,8, 10,11,12,13,14,15, 21, 24, 29, 31, 36, 37, 41,42,43,44,45] and references therein.
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