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On some properties of Jensen-Steffensen’s functional. (English) Zbl 1249.26028
Summary: Motivated by results of S. S. Dragomir, related to superadditivity and monotonicity of discrete Jensen’s functional, we consider Jensen-Steffensen’s functional, i.e., Jensen’s functional with the conditions derived from Jensen-Steffensen’s inequality. We state and prove results for this functional, similar to those of Dragomir, as well as their integral versions. Finally, some applications concerning means are given.

MSC:
26D10 Inequalities involving derivatives and differential and integral operators
26A51 Convexity of real functions in one variable, generalizations
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