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A note on multivariate Ostrowski type inequalities *.(Report)

In this note, we establish some multivariate Ostrowski type inequalities involving several functions.

Keywords and Phrases: Multivariate, Ostrowski type inequalities, n-fold integral.

1. Introduction

Throughout, R and [R.sup.n] denote the set of real numbers and the n--dimensional Euclidean space, respectively. Let D = {([x.sub.1], ..., [x.sub.n])[member of] [R.sup.n]: [a.sub.i]

In 1938, Ostrowski [3, p.468] established the following integral inequality:

Let f: [a, b] [right arrow] R be continuous on [a, b] and differentiable on (a, b). If the derivative f' is bounded on (a, b), that is,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

then

[MATHEMATICAL ...

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