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 H�lder’s inequality with weights satisfying the conditions as in the Jensen-Steffensen
inequality. A few well-known inequalities for quasi-arithmetic means are generalized.
A sequence of inequalities which include McShane’s generalization of Jensen’s inequality for isotonic positive linear functionals
and convex functions are proved and compared with results in . As applications some results for the means are pointed out.
Moreover, further inequalities of Hölder type are presented.