On the Jensen-Steffensen inequality for generalized convex functions
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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.
Key words and phrasesP-convex functions functions with nondecreasing increments Jensen-Steffensen inequality Čebyšev’s inequality Hölder’s inequality generalized quasiarithmetic means
Mathematics subject classification number26D15 26B25
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