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A note on an Ostrowski type inequality *.(Report)

Calculate a definite integral by transforming it to a double integral and then changing the order of integration. Thus provide a neat error bound of an Ostrowski type inequality in the literature.

Keywords and Phrases: Montgomery identity, Ostrowski type inequality, Double integral.

As the first main result in (1), G.A. Anastassiou presented the following Ostrowski type inequality.

Theorem A. Let f: [a, b] [right arrow] R be 3-times differentiable on (a, b) whose third derivative f''': (a, b) [right arrow] R is bounded on (a, b), i.e., [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Then we have the inequality

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

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