Normalized Jensen Functional, Superquadracity and Related Inequalities
نویسندگان
چکیده
In this paper we generalize the inequality MJn (f,x,q) ≥ Jn (f,x,p) ≥ mJn (f,x,q) where Jn (f,x,p) = n ∑ i=1 pif (xi)− f ( n ∑ i=1 pixi ) , obtained by S.S. Dragomir for convex functions. We provide cases where we can improve the bounds m and M for convex functions, and also, we show that for the class of superquadratic functions nonzero lower bounds of Jn (f,x,p)− mJn (f,x,q) and nonzero upper bounds of Jn (f,x,p)−MJn (f,x,q) can be pointed out. Finally, an inequality related to the Čebyšev functional and superquadracity is also given.
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