On the nonexistence of some interpolatory polynomials.
On the order of approximation of functions by the bidimensional operators Favard-Szász-Mirakyan.
On the quantitative Fatou property
The result of this article together with [1] and [4] gives a full quantitative description of a Fatou type property for functions from Hardy classes in the upper half plane.
On the rate of approximation in the random sum CLT for dependent variables
Capital and lower-case approximations of the expected value of a class of smooth functions of the normalized random partial sums of dependent random variables by the expectation of the corresponding functions of Gaussian random variables are established. The same types of approximation are also obtained for dependent random vectors. This generalizes and improves previous results of the author (1980) and Rychlik and Szynal (1979).
On the rate of convergence for bivariate Beta operators.
On the rate of convergence for modified Szász-Mirakyan operators on functions of bounded variation.
On the rate of convergence of Hermite-Fejér polynomials to functions of bounded variation on the zeros of certain Jacobi polynomials
On the rate of convergence of some orthogonal polynomial expansions.
On the rate of pointwise convergence of Szász-Mirakyan operators
On the rate of strong summability by matrix means in the generalized Hölder metric.
On the rate of summability by matrix means in the generalized Hölder metric
We will generalize and improve the results of T. Singh [Publ. Math. Debrecen 40 (1992), 261-271] obtaining the L. Leindler type estimates from [Acta Math. Hungar. 104 (2004), 105-113].
On the Sharpness of Non-Optimal Approximation for Semigroup Operators.
On uniform convergence for (mu,nu)-type rational approximants in II.
On weighted -approximation by polynomials
Optimal problems concerning interpolation methods of solution of equations.
Order of approximation of functions of two variables by new type gamma operators.
Penalized Least Squares Fitting
* Supported by the Army Research Office under grant DAAD-19-02-10059.Bounds on the error of certain penalized least squares data fitting methods are derived. In addition to general results in a fairly abstract setting, more detailed results are included for several particularly interesting special cases, including splines in both one and several variables.
Pointwise approximation by Meyer-König and Zeller operators
We study the rate of pointwise convergence of Meyer-König and Zeller operators for bounded functions, and get an asymptotically optimal estimate.
Pointwise estimates for modified positive linear operators
Pointwise inequalities and approximation in fractional Sobolev spaces
We prove that a function belonging to a fractional Sobolev space may be approximated in capacity and norm by smooth functions belonging to , 0 < m + λ < α. Our results generalize and extend those of [12], [4], [14], and [11].