Bounds for the Normalized Jensen – Mercer Functional
نویسنده
چکیده
We introduce the normalized Jensen-Mercer functional Mn( f ,x, p) = f (a)+ f (b)− n ∑ i=1 pi f (xi)− f ( a+b− n ∑ i=1 pixi ) and establish the inequalities of type MMn( f ,x,q) Mn( f ,x, p) mMn( f ,x,q) , where f is a convex function, x = (x1, . . . ,xn) and m and M are real numbers satisfying certain conditions. We prove them for the case when p and q are nonnegative n -tuples and when p and q satisfy the conditions for the Jensen-Steffensen inequality. We also give their integral versions in both cases.
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