Polynomial approximation and twenty years later.
Polynomial inequalities on algebraic sets
We give an estimate of Siciak’s extremal function for compact subsets of algebraic varieties in (resp. ). As an application we obtain Bernstein-Walsh and tangential Markov type inequalities for (the traces of) polynomials on algebraic sets.
Properties of a new class of recursively defined Baskakov-type operators
By starting from a recent paper by Campiti and Metafune [7], we consider a generalization of the Baskakov operators, which is introduced by replacing the binomial coefficients with other coefficients defined recursively by means of two fixed sequences of real numbers. In this paper, we indicate some of their properties, including a decomposition into an expression which depends linearly on the fixed sequences and an estimation of the corresponding order of approximation, in terms of the modulus...
Properties of -Meyer-König-Zeller Durrmeyer operators.
Properties of some bivariate approximants.
The smoothness and approximation properties of certain discrete operators for bivariate functions are examined.
-parametric Bleimann Butzer and Hahn operators.
Quartic X-Splines.
Quasi-greedy bases and Lebesgue-type inequalities
We study Lebesgue-type inequalities for greedy approximation with respect to quasi-greedy bases. We mostly concentrate on the spaces. The novelty of the paper is in obtaining better Lebesgue-type inequalities under extra assumptions on a quasi-greedy basis than known Lebesgue-type inequalities for quasi-greedy bases. We consider uniformly bounded quasi-greedy bases of , 1 < p < ∞, and prove that for such bases an extra multiplier in the Lebesgue-type inequality can be taken as C(p)ln(m+1)....
Rate of convergence for a general sequence of Durrmeyer type operators.
Rate of convergence of beta operators of second kind for functions with derivatives of bounded variation.
Rate of convergence of Chlodowsky operators for functions with derivatives of bounded variation.
Rate of convergence of Chlodowsky type Durrmeyer operators.
Rate of convergence of some neural network operators to the unit-univariate case, revisited
Rate of convergence of summation-integral type operators with derivatives of bounded variation.
Rate of convergence of the discrete Pólya algorithm from convex sets. A particular case.
Rate of convergence on Baskakov-Beta-Bézier operators for bounded variation functions.
Rates of Convergence for the Approximation of Dual Shift-Invariant Systems in ... (...).
Rates of convergence of Chlodovsky-Kantorovich polynomials in classes of locally integrable functions
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.
Reflections on Value Regions, Limit Regions and Truncation Errors for Continued Fractions.
Remarks on an article of J.P. King
The present note discusses an interesting positive linear operator which was recently introduced by J.P. King. New estimates in terms of the first and second modulus of continuity are given, and iterates of the operators are considered as well. For general King operators the second moments are minimized.