A refinement of Holder's integral inequality
2003 ◽
Vol 34
(4)
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pp. 383-386
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Keyword(s):
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$.
2021 ◽
Vol 7
(1)
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pp. 88-99
1989 ◽
Vol 12
(1)
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pp. 9-13
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Keyword(s):
1989 ◽
Vol 32
(4)
◽
pp. 417-424
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2005 ◽
Vol 178
◽
pp. 55-61
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