Inequalities of Jensen and Chebyshev Type for Interval-Valued Measures Based on Pseudo-integrals

Inequalities of the Chebyshev type based on pseudo-integrals

“…The notions of pseudo-operations and pseudo-integration are given through some essential examples. We also give a short overview of the results from [13][14][15]26,27,33].…”

“…and α ∈ [a, b] + , using the definition of pseudo-operations defined on non-empty subsets of [a, b] + (see [13,29]), then in the case when ⊕ = max or when g is an increasing function, we get…”

“…The generalizations of different classical integral inequalities in the frame of the pseudo-analysis, such as Minkowski, Hölder, Berwald, Jensen and Cauchy-Schwarz inequalities were studied in [2][3][4]8,13]. All of these indicate the importance and usefulness of researching this type of inequalities, especially due to the frequent applications in the decision theory, premium principle, probability theory etc.…”

“…Another interesting study of the pseudo-integral of a setvalued function and the pseudo-integral on an interval-valued function is given in [14,15]. Also, one more type of interval-valued pseudo-integral is studied in [13].…”

“…The inequality of the Chebyshev type has been studied in [1,12,13,29,30,32]. The generalizations of different classical integral inequalities in the frame of the pseudo-analysis, such as Minkowski, Hölder, Berwald, Jensen and Cauchy-Schwarz inequalities were studied in [2][3][4]8,13].…”