Узагальнені обернені нерівності Єнсена-Штеффенсена та пов’язані нерівності

Abstract

We compare two linear functionals that are negative on convex functions. Further, using Green's functions we give some new conditions for reversed Jensen-Steffensen and related inequalities to hold. Using Green's function we also give refinement of Levinson type generalization of reversed Jensen-Steffensen and related inequalities. The acquired results are then used for constructing mean-value theorems.