engleski

On the refinements of the integral Jensen-Steffensen inequality

In this paper, we present integral versions of some recently proved results which refine the Jensen-Steffensen inequality. We prove the n- exponential convexity and log-convexity of the functions associated with the linear functionals constructed from the refined inequalities and also prove the monotonicity property of the generalized Cauchy means. Finally, we give several examples of the families of functions for which the results can be applied.

convex function ; Jensen-Steffensen weighted integral inequality ; n-exponential and logarithmic convexity ; mean value theorems ; divided difference

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