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Generalizations of Jensen-Steffensen and related integral inequalities for superquadratic functions

Shoshana AbramovichSlavica IvelićJosip Pečarić — 2010

Open Mathematics

We present integral versions of some recently proved results which improve the Jensen-Steffensen and related inequalities for superquadratic functions. For superquadratic functions which are not convex we get inequalities analogous to the integral Jensen-Steffensen inequality for convex functions. Therefore, we get refinements of all the results which use only the convexity of these functions. One of the inequalities that we obtain for a superquadratic function φ is y ¯ φ x ¯ + 1 λ β - λ α α β φ f t - x ¯ d λ t , where x ¯ = 1 λ β - λ α α β f t d λ t and y ¯ = 1 λ β - λ α α β φ f t d λ t which under...

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