Inequalities for the area balance of absolutely continuous functions
DOI:
https://doi.org/10.24193/subbmath.2018.1.03Keywords:
Functions of bounded variation, Lipschitzian functions, convex functions, integral inequalities.Abstract
We introduce the area balance function associated to a Lebesgue integrable function f : [a, b] → C by ABf (a, b, ·) : [a, b] → C, ABf (a, b, x) := x f (t) dt − x l (t) dt . a We show amongst other that, if f : I → C is an absolutely continuous function on the interval I and [a, b] ⊂ ˚I, where ˚I is the interior of I and such that fl is of bounded variation on [a, b] , then we have the inequality...
Mathematics Subject Classification (2010): 26D15, 25D10.
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