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I am searching for an upper bound of exponential function (or sum of experiential functions):

1) [tex]\exp(x)\leq f(x)[/tex]

or:

2) [tex]\sum_{i=1}^n \exp(x_i) \leq f(x_1,\cdots,x_n, n)[/tex] .

Since exponential function is convex, it is not possible to use Jenssen's inequality to get an upper bound like 2). Does anyone has an ideal?

Thanks a lot!