Iterates of Bernstein operators, via contraction principle

Iterates of a class of discrete linear operators via contraction principle

In this paper we are concerned with a general class of positive linear operators of discrete type. Based on the results of the weakly Picard operators theory our aim is to study the convergence of the iterates of the defined operators and some approximation properties of our class as well. Some special cases in connection with binomial type operators are also revealed.

Iterates of Conditional Expectation Operators

On the Convergence and Iterates of q-Bernstein Polynomials

The convergence properties of q-Bernstein polynomials are investigated. When q > 1 is fixed the generalized Bernstein polynomials Bnf of f , a one parameter family of Bernstein polynomials, converge to f as n → ∞ if f is a polynomial. It is proved that, if the parameter 0 < q < 1 is fixed, then Bnf → f if and only if f is linear. The iterates of Bnf are also considered. It is shown that B n f c...

Iterates of Volterra operators and indeterminate forms

During the last decades, many attempts have beenmade in order to explain and formalize mathematically a large set of phenomena that, at a first glance, are not well described by traditional theories. Among those attempts one finds the whole theory of self-organized criticality and some statistical theories. In recent years, a popular approach has been a Daróczy-like entropy [2] and its correspo...

Optimality of generalized Bernstein operators

We show that a certain optimality property of the classical Bernstein operator also holds, when suitably reinterpreted, for generalized Bernstein operators on extended Chebyshev systems.