Abstract
In this paper we obtain sharp Ostrowski type inequalities for multidimensional sets of bounded variation and multivariate functions of bounded variation.
Highlights
In Ostrowski [ ] proved the following inequality.Theorem Let f : [, ] → R be a differentiable on (, ) function with bounded on (, ) derivative
See [ ] and the references therein for results connected with Ostrowski type inequalities for univariate functions of bounded variation and their applications
We introduce a new definition of bounded variation that is based on the KronrodVitushkin approach [ ]
Summary
In Ostrowski [ ] proved the following inequality.Theorem Let f : [ , ] → R be a differentiable on ( , ) function with bounded on ( , ) derivative. Lemma For an arbitrary function f : E → R, denote by Textr the set of t ∈ R such that L(f ; t) contains an extremum point.
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