Displaying similar documents to “Differences of weighted mixed symmetric means and related results.”

Generalizations of the Jensen-Steffensen and related inequalities

Milica Bakula, Marko Matić, Josip Pečarić (2009)

Open Mathematics

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We present a couple of general inequalities related to the Jensen-Steffensen inequality in its discrete and integral form. The Jensen-Steffensen inequality, Slater’s inequality and a generalization of the counterpart to the Jensen-Steffensen inequality are deduced as special cases from these general inequalities.

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

Shoshana Abramovich, Slavica Ivelić, Josip Pečarić (2010)

Open Mathematics

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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...

Accentuate the negative

P. S. Bullen (2009)

Mathematica Bohemica

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A survey of mean inequalities with real weights is given.