engleski

More accurate Jensen-type inequalities for signed measures

In this talk we give improvements of several Jensen-type inequalities, giving the necessary and sufficient conditions for them to hold in case of the real Stieltjes measure d \lambda, not necessarily positive. As an application, we derive corresponding mean-value theorems, investigate the exponential and logarithmic convexity of the differences between the left-hand and the right-hand side of the obtained inequalities, also giving several examples of the families of functions for which those results can be applied.

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

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