Inequalities on General Lp-Mixed Chord Integral Difference

General Lp-mixed width-integral of convex bodies and related inequalities

The conception of general Lp-mixed width-integral of convex bodies is introduced and related isoperimetric type inequality, Aleksandrov-Fenchel type inequality and a cyclic inequality are established. Further, the extremum values for the general Lpmixed width-integral are obtained. c ©2017 All rights reserved.

Inequalities for General Integral Means

We modify the definition of the weighted integral mean so that we can compare two such means not only upon the main function but also upon the weight function. As a consequence, some inequalities between means are proved.

Difference of General Integral Means

In this paper we present sharp estimates for the difference of general integral means with respect to even different finite measures. This is achieved by the use of the Ostrowski and Fink inequalities and the Geometric Moment Theory Method. The produced inequalities are with respect to the supnorm of a derivative of the involved function.

General Chebyshev type inequalities for universal integral

A new inequality for the universal integral on abstract spaces is obtained in a rather general form. As two corollaries, Minkowski’s and Chebyshev’s type inequalities for the universal integral are obtained. The main results of this paper generalize some previous results obtained for special fuzzy integrals, e.g., Choquet and Sugeno integrals. Furthermore, related inequalities for seminormed in...

Affine inequalities for Lp$L_{p}$-mixed mean zonoids