منابع مشابه
Nearly Comonotone Approximation
We discuss the degree of approximation by polynomials of a function f that is piecewise monotone in ?1; 1]. We would like to approximate f by polynomials which are comonotone with it. We show that by relaxing the requirement for comonotonicity in small neighborhoods of the points where changes in monotonicity occur and near the endpoints, we can achieve a higher degree of approximation. We show...
متن کاملNearly Comonotone Approximation Ii
When we approximate a continuous function f which changes its monotonicity nitely many, say s times, in ?1; 1], we wish sometimes that the approximating polynomials follow these changes in monotonicity. However, it is well known that this requirement restricts very much the degree of approximation that the polynomials can achieve, namely, only the rate of ! 2 (f; 1=n) and even this not with a c...
متن کاملPositive Results and Counterexamples in Comonotone Approximation
We estimate the degree of comonotone polynomial approximation of continuous functions f , on [−1,1], that change monotonicity s ≥ 1 times in the interval, when the degree of unconstrained polynomial approximation En(f ) ≤ n−α , n ≥ 1. We ask whether the degree of comonotone approximation is necessarily ≤ c(α, s)n−α , n ≥ 1, and if not, what can be said. It turns out that for each s ≥ 1, there i...
متن کاملComonotone Pareto Optimal Allocations for Law Invariant
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...
متن کاملComonotone maxitivity and extended Sugeno integral
Comonotone maxitive idempotent aggregation functions on [0, 1] are characterized and the extended Sugeno integral is introduced. Also the relationship of Sugeno integral and the extended Sugeno integral is clarified. Finally, extended weighted maxima on [0, 1] are discussed.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1999
ISSN: 0021-9045
DOI: 10.1006/jath.1999.3327