Research articles
ScienceAsia 50 (2024):ID 2024059 1-6 |doi:
10.2306/scienceasia1513-1874.2024.059
Further multi-term refinements of Youngs type inequalities
and its applications
ChangSen Yang, YaNan Wang*
ABSTRACT: We obtain some refined Young?s type inequalities in this paper. And the results are given as follows. Let
a, b > 0, 0 ? ? ? ? ? 1, then for any positive integer N: if m
2N < ? ? ? ?
m+1
2N for m ? {0, 1, 2, ??? , 2N ? 1}, we have
a?? b ? K
2
N ??m
2
N? b
a
, 2
a?? b +
XN?1
l=0
rl
(?)
2Xl
k=1
q
a
1?
k?1
2l b
k?1
2l ?
q
a
1?
k
2l b
k
2l
2
X
k?1
2l
,
k
2l
(?)
+
2
N ? ? m
2N ? ? m
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a |
School of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan 453007 China |
* Corresponding author, E-mail: 15517376731@163.com
Received 4 Jun 2023, Accepted 17 May 2024
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