A refinement of Holder's integral inequality

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Zheng Liu


The purpose of this note is to show that there is monotonic continuous function $ p(t)$ such that

$$ \int_a^b \left(\prod_{i=1}^n f_i(x)\right) dx\le p(t)\le \prod_{i=1}^n  \left(\int_a^b f_i^{r_i}(x)dx \right)^{1\over r_i},$$

where $ f_1$, $ f_2,\ldots,f_n$ are real positive continuous functions on $ [a,b]$ and $ r_1$, $ r_2,\ldots,r_n$ are real positive numbers with $ \sum_{i=1}^n {1\over r_i}=1$.

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How to Cite
Liu, Z. (2003). A refinement of Holder’s integral inequality. Tamkang Journal of Mathematics, 34(4), 383–386. https://doi.org/10.5556/j.tkjm.34.2003.240
Author Biography

Zheng Liu

Institute of Applied Mathematics, Faculty of Science, Anshan University of Science and Technology, Anshan 114044, Liaoning, P. R. China.