Let f ∈ C[−1, 1] change its convexity finitely many times, in the interval. We are interested in estimating the degree of approximation of f by polynomials, and by piecewise polynomials, which are coconvex with it, namely, polynomials and piecewise polynomials that change their convexity exactly at the points where f does. We obtain Jackson type estimates and summarize the positive and negative...

Let En(f) denote the degree of approximation of f ∈ C[−1, 1], by algebraic polynomials of degree < n, and assume that we know that for some α > 0 and N ≥ 2, nEn(f) ≤ 1, n ≥ N. Suppose that f changes its monotonicity s ≥ 1 times in [−1, 1]. We are interested in what may be said about its degree of approximation by polynomials of degree < n that are comonotone with f . In particular, if f changes...

In this paper, first, we extend the analytical expression of optimal solution constrained OWA aggregation problem with two comonotone constraints by also including case when weights are arbitrary non-negative numbers. Then, indicate an iterative algorithm that precisely indicates whether a constraint in auxiliary is either biding or strictly redundant. Actually, (or constraints, as may occur) e...

Based on the method of copulas, we construct a parametric family of multivariate distributions using mixtures of independent conditional distributions. The new family of multivariate copulas is a convex combination of products of independent and comonotone subcopulas. It fulfills the four most desirable properties that a multivariate statistical model should satisfy. In particular, the bivariat...

In this paper we prove the existence of Pareto optimal allocations of integrable random endowments when decision makers have probabilistic sophisticated variational preferences. Variational preferences were introduced and axiomatically characterized by Maccheroni, Marinacci, and Rustichini (2006). This broad class of preferences allows to model ambiguity aversion and includes several subclasses...

This paper explores risk-sharing and equilibrium in a general equilibrium set-up wherein agents are non-additive expected utility maximizers. We show that when agents have the same convex capacity, the set of Pareto-optima is independent of it and identical to the set of optima of an economy in which agents are expected utility maximizers and have same probability. Hence, optimal allocations ar...

In this paper, some results of the Chebyshev type integral inequality for the pseudo-integral are proven. The obtained results, are related to the measure of a level set of the maximum and the sum of two non-negative integrable functions. Finally, we applied our results  to the case of comonotone functions.