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IMC
1995 IMC
6
6
Part of
1995 IMC
Problems
(1)
IMC 1995 Problem 6
Source: IMC 1995
2/18/2021
Let
p
>
1
p>1
p
>
1
. Show that there exists a constant
K
p
>
0
K_{p} >0
K
p
>
0
such that for every
x
,
y
∈
R
x,y\in \mathbb{R}
x
,
y
∈
R
with
∣
x
∣
p
+
∣
y
∣
p
=
2
|x|^{p}+|y|^{p}=2
∣
x
∣
p
+
∣
y
∣
p
=
2
, we have
(
x
−
y
)
2
≤
K
p
(
4
−
(
x
+
y
)
2
)
.
(x-y)^{2} \leq K_{p}(4-(x+y)^{2}).
(
x
−
y
)
2
≤
K
p
(
4
−
(
x
+
y
)
2
)
.
inequalities
real analysis