An inequality for a two variable function

  • Thread starter amirmath
  • Start date
  • #1
8
0
Suppose that ##F(u,v)=a|u+v|^{r+1}+2b|uv|^{\frac{r+1}{2}}##, where ##a>1, b>0## and ##r\geq3.## How we can show that there exists a positive constant c such that
##
F(u,v)\geq c\Big( |u|^{r+1}+|v|^{r+1}\Big).
##
 

Answers and Replies

  • #2
Simon Bridge
Science Advisor
Homework Helper
17,857
1,655
You'd start by considering what sort of curve is described by the part in parentheses in the second relation.
What role does c play? Is there a minimum value that the first expression can take?
 

Related Threads on An inequality for a two variable function

Replies
3
Views
701
Replies
1
Views
804
  • Last Post
Replies
1
Views
2K
Replies
1
Views
978
  • Last Post
Replies
1
Views
1K
Replies
8
Views
910
  • Last Post
Replies
9
Views
5K
Replies
2
Views
3K
Replies
3
Views
5K
Top