engleski

Uniform treatment of Jensen-type inequalities using several different Green functions

The main purpose of this work is to give the uniform treatment of the Jensen type inequalities. Using different Green functions, we give new conditions for Jensen's inequality to hold in case of the real Stieltjes measure d \lambda, which is not necessarily positive. Using the same method we also give adequate results for the converses of the Jensen inequality and as a consequence we get the results concerning the Hermite-Hadamard inequality. We also give some further interesting results and applications.

Jensen inequality ; Green function ; Hermite-Hadamard inequality

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