Y by Adventure10
Hello,
Here I am going to discuss a new theory and a quite useful way of solving inequality problems in which we use the Rearrangement inequality as a tool to develop a new type of inequality the Functional Reciprocal Sum inequality which is described as follows :
This work is authored by Aditya Guha Roy
If for a function over some subset we have
the pairs and are similarly sorted then we say that
is p-monotone over .
And if ,
the pairs and are oppositely sorted then we say that
is i-monotone over .
With this we have some lemmas :
Lemma 1 : (First Functional Reciprocal Sum Inequality (FRS 1)
If is p-monotone over and is i-monotone over then, we have the following inequality :
Can we extend this to variables ?
If yes, how ?
Please help !!
Here I am going to discuss a new theory and a quite useful way of solving inequality problems in which we use the Rearrangement inequality as a tool to develop a new type of inequality the Functional Reciprocal Sum inequality which is described as follows :
This work is authored by Aditya Guha Roy
If for a function over some subset we have
the pairs and are similarly sorted then we say that
is p-monotone over .
And if ,
the pairs and are oppositely sorted then we say that
is i-monotone over .
With this we have some lemmas :
Lemma 1 : (First Functional Reciprocal Sum Inequality (FRS 1)
If is p-monotone over and is i-monotone over then, we have the following inequality :
Can we extend this to variables ?
If yes, how ?
Please help !!
This post has been edited 4 times. Last edited by adityaguharoy, Nov 22, 2016, 3:45 AM