engleski

More accurate Jensen-type inequalities for signed measures characterized via Green function and applications

In this paper we derive several improved forms of the Jensen inequality, giving the necessary and sufficient conditions for them to hold in case of the real Stieltjes measure, not necessarily positive. The obtained relations are characterized via the Green function. As an application, our main results are employed for constructing some classes of exponentially convex functions and some Cauchy-type means.

Jensen inequality ; Green function ; refinement ; convex function ; exponetially convex function ; Cauchy-type mean

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