On exponential convexity, Jensen-Steffensen-Boas Inequality, and Cauchy's means for superquadratic functions

On the Jensen-Steffensen inequality for generalized convex functions

Jensen–Steffensen type inequalities for P -convex functions and functions with nondecreasing increments are presented. The obtained results are used to prove a generalization of Čebyšev’s inequality and several variants of Hölder’s inequality with weights satisfying the conditions as in the Jensen–Steffensen inequality. A few well-known inequalities for quasi-arithmetic means are generalized.

On the refinements of the Jensen-Steffensen inequality

* Correspondence: [email protected] Abdus Salam School of Mathematical Sciences, GC University, 68-b, New Muslim Town, Lahore 54600, Pakistan Full list of author information is available at the end of the article Abstract In this paper, we extend some old and give some new refinements of the JensenSteffensen inequality. Further, we investigate the log-convexity and the exponential conve...

A Variant of Jensen-steffensen’s Inequality for Convex and Superquadratic Functions

A variant of Jensen-Steffensen’s inequality is considered for convex and for superquadratic functions. Consequently, inequalities for power means involving not only positive weights have been established.

Generalized Steffensen Means

A Steffensen Type Inequality

Steffensen’s inequality deals with the comparison between integrals over a whole interval [a, b] and integrals over a subset of [a, b]. In this paper we prove an inequality which is similar to Steffensen’s inequality. The most general form of this inequality deals with integrals over a measure space. We also consider the discrete case.