Inequalities of Chebyshev Type Involving Conditional Expectations

Chebyshev type inequalities by means of copulas

A copula is a function which joins (or 'couples') a bivariate distribution function to its marginal (one-dimensional) distribution functions. In this paper, we obtain Chebyshev type inequalities by utilising copulas.

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...

Three Mappings Related to Chebyshev-type Inequalities

In this paper, by the Chebyshev-type inequalities we define three mappings, investigate their main properties, give some refinements for Chebyshev-type inequalities, obtain some applications.

Chebyshev type inequalities for pseudo-integrals

Chebyshev and Grüss Type Inequalities Involving Two Linear Functionals and Applications

In the present paper we prove the Chebyshev inequality involving two isotonic linear functionals. Namely, if A and B are isotonic linear functionals, then A(p f g)B(q)+A(p)B(q f g) A(p f )B(qg) + A(pg)B(q f ) , where p,q are non-negative weights and f ,g are similarly ordered functions such that the above-mentioned terms are well-defined. If functionals are equal, i.e. A = B and if p = q , then...