engleski

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.

P-convex functions; functions with nondecreasing increments; Jensen-Steffensen inequality; Čebyšev's inequality; Hölder's inequality; generalized quasi-arithmetic means.

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