In this paper we establish an estimation for the rate of pointwise convergence of the Chlodovsky-Kantorovich polynomials for functions f locally integrable on the interval [0,∞). In particular, corresponding estimation for functions f measurable and locally bounded on [0,∞) is presented, too.
2
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
Starting from a differential equation \(\frac{\partial}{\partial t} W (\lambda, t, u)=\frac{\lambda(u-t)}{p(t)}W(\lambda,t,u)-\beta W(\lambda,t,u)\) for the kernel of an operator \(S_\lambda(f,t) = \int_{A}^{B}W(\lambda,t,u)f(u)du\) with the normalization condition \(\int_A^B W(\lambda, t, u)du = 1\) we prove some properties which are similar to properties proved by Ismail and May for the exponential operators. In particular, we show that all these operators are approximation operators. Moreover, a method of determining \(S_\lambda\) for a given function \(p\) is introduced.
In the present paper we consider the Bézier variant of Chlodovsky-Kantorovich operators \(K_{n−1,\alpha} f\) for functions \(f\) measurable and locally bounded on the interval \([0,\infty)\). By using the Chanturiya modulus of variation we estimate the rate of pointwise convergence of \(K_{n−1,\alpha} f (x)\) at those \(x \gt 0\) at which the one-sided limits \(f (x+)\), \(f(x-)\) exist.
The aim of this paper is to study a bivariate version of the operator investigated in [2], [4]. We shall present Voronovskaya type theorem and theorems giving a rate of convergence of this operator. Some applications for the limit problem are indicated.
6
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
Some general representation formulae for (C₀) m-parameter operator semigroups with rates of convergence are obtained by the probabilistic approach and multiplier enlargement method. These cover all known representation formulae for (C₀) one- and m-parameter operator semigroups as special cases. When we consider special semigroups we recover well-known convergence theorems for multivariate approximation operators.
7
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
Using tools of approximation theory, we evaluate rates of bias convergence for sequences of generalized L-statistics based on i.i.d. samples under mild smoothness conditions on the weight function and simple moment conditions on the score function. Apart from standard methods of weighting, we introduce and analyze L-statistics with possibly random coefficients defined by means of positive linear functionals acting on the weight function.
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.