An equivalent condition to the Jensen inequality for the generalized Sugeno integral.

For the classical Jensen inequality of convex functions, i.e., [Formula: see text] an equivalent condition is proved in the framework of the generalized Sugeno integral. Also, the necessary and sufficient conditions for the validity of the discrete form of the Jensen inequality for the generalized Sugeno integral are given

General related jensen type inequalities for fuzzy integrals

In this paper, related inequalities to Jensen type inequality for the seminormed fuzzy integrals are studied. Several examples are given to illustrate the validity of theorems. Some results on Jensen type inequalities are obtained.Publisher's Versio

The Choquet integral as Lebesgue integral and related inequalities

summary:The integral inequalities known for the Lebesgue integral are discussed in the framework of the Choquet integral. While the Jensen inequality was known to be valid for the Choquet integral without any additional constraints, this is not more true for the Cauchy, Minkowski, Hölder and other inequalities. For a fixed monotone measure, constraints on the involved functions sufficient to guarantee the validity of the discussed inequalities are given. Moreover, the comonotonicity of the considered functions is shown to be a sufficient constraint ensuring the validity of all discussed inequalities for the Choquet integral, independently of the underlying monotone measure

Investigation of a Stolarsky type Inequality for Integrals in Pseudo-Analysis

MSC 2010: 03E72, 26E50, 28E10In this paper, we prove a Stolarsky type inequality for pseudo-integrals