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Article: A note on an Ostrowski type inequality *.(Report)
- Article from:
- Tamsui Oxford Journal of Mathematical Sciences
- Article date:
- May 1, 2008
- Author:
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Copyright informationCOPYRIGHT 2008 Aletheia University. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information)
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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]
for every x [member of] [a, b], where
A(x): = [abx.sup.4] - [[1/3][a.sup.2][b.sup.3]x] + [[1/3][a.sup.3][bx.sup.2]] - [[ab.sup.2][x.sup.3]] - [[1/3][a.sup.3][b.sup.2]x] + [[1/3][ab.sup.3][x.sup.2]] + [[a.sup.2][b.sup.2][x.sup.2]] - [[a.sup.2][bx.sup.3]] - [[1/2][ax.sup.5]] - ...
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