I'm stuck on a matter related to my research.
Are there any results done on when one order of composition of functions is bigger than another? More specifically, for which functions f and g does
f(g(x)) > g(f(x))?
Are there any specific classes of functions for which this holds?
The functions I'm considering are also convex and non-decreasing if that is relevant. Thanks.
Square root and exponential are two such functions. √ (e^x) > e ^ √x
For x>4.