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Extended normalized Jensen functional related to convexity, 1-quasiconvexity and superquadracity. (English) Zbl 1403.26017

Summary: In this paper we extend results related to normalized Jensen functional in several directions. We compare a specific Jensen functional with a sum of other functionals for convex functions, and we also extend these results for 1-quasiconvex functions and for superquadratic functions.

MSC:

26D15 Inequalities for sums, series and integrals
26A51 Convexity of real functions in one variable, generalizations
26B25 Convexity of real functions of several variables, generalizations
39B62 Functional inequalities, including subadditivity, convexity, etc.
47A63 Linear operator inequalities
47A64 Operator means involving linear operators, shorted linear operators, etc.
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