Parabolic partial differential equation: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older edit
No edit summary
en>Trappist the monk
m →References: replace mr template with mr parameter in CS1 templates; using AWB
 
(One intermediate revision by one other user not shown)
Line 1: Line 1:
In [[mathematics]], '''Levinson's inequality ''' is the following inequality, due to [[Norman Levinson]], involving positive numbers. Let <math>a>0</math> and let <math>f</math> be a given function having a third derivative on the range <math>(0,2a)</math>, and such that
Nice to meet you, I am Marvella Shryock. To play baseball is the pastime he will by no means quit doing. South Dakota is her beginning place but she requirements to transfer simply because of her family members. I am a meter reader but I strategy on altering it.<br><br>My webpage: [http://www.pornextras.info/blog/187567 home std test kit]
 
:<math>f'''(x)\geq 0</math>
 
for all <math>x\in (0,2a)</math>. Suppose <math>0<x_i\leq a</math> for <math> i = 1, \ldots, n</math> and <math>0<p</math>.  Then
 
: <math>\frac{\sum_{i=1}^np_i f(x_i)}{\sum_{i=1}^np_i}-f\left(\frac{\sum_{i=1}^np_ix_i}{\sum_{i=1}^np_i}\right)\le\frac{\sum_{i=1}^np_if(2a-x_i)}{\sum_{i=1}^np_i}-f\left(\frac{\sum_{i=1}^np_i(2a-x_i)}{\sum_{i=1}^np_i}\right).</math>
 
The [[Ky Fan inequality]] is the special case of Levinson's inequality where
 
:<math>p_i=1,\  a=\frac{1}{2},</math>
 
and
 
:<math>f(x)=\log x. \, </math>
 
==References==
*Scott Lawrence and Daniel Segalman: ''A generalization of two inequalities involving means'', Proceedings of the American Mathematical Society. Vol 35 No. 1, September 1972.
*Norman Levinson: ''Generalization of an inequality of Ky Fan'', Journal of Mathematical Analysis and Applications. Vol 8 (1964), 133–134.
 
[[Category:Inequalities]]

Latest revision as of 14:23, 25 September 2014

Nice to meet you, I am Marvella Shryock. To play baseball is the pastime he will by no means quit doing. South Dakota is her beginning place but she requirements to transfer simply because of her family members. I am a meter reader but I strategy on altering it.

My webpage: home std test kit

Retrieved from "https://en.formulasearchengine.com/index.php?title=Parabolic_partial_differential_equation&oldid=251054"