Linear operators that preserve some test functions.
Local approximation properties of certain class of linear positive operators via I-convergence
In this study, we obtain a local approximation theorems for a certain family of positive linear operators via I-convergence by using the first and the second modulus of continuities and the elements of Lipschitz class functions. We also give an example to show that the classical Korovkin Theory does not work but the theory works in I-convergence sense.
Lototsky-Schnabl Operators on Compact Convex Sets and Their Associated Limit Semigroups.
Mixed K-Functionals: A Measure of Smoothness for Blending-type Approximation.
Mixed norm condition numbers for the univariate Bernstein basis
We study mixed norm condition numbers for the univariate Bernstein basis for polynomials of degree n, that is, we measure the stability of the coefficients of the basis in the -sequence norm whereas the polynomials to be represented are measured in the -function norm. The resulting condition numbers differ from earlier results obtained for p = q.
Nonnegative order iterates of Bernstein polynomials and their limiting semigroup
Note on universal algorithms for learning theory
We study the universal estimator for the regression problem in learning theory considered by Binev et al. This new approach allows us to improve their results.
On a class of Szász-Mirakyan type operators
The actual construction of the Szász-Mirakyan operators and its various modifications require estimations of infinite series which in a certain sense restrict their usefulness from the computational point of view. Thus the question arises whether the Szász-Mirakyan operators and their generalizations cannot be replaced by a finite sum. In connection with this question we propose a new family of linear positive operators.
On a family of linear and positive operators in weighted spaces.
On a general class of Beta approximating operators.
On a general class of linear and positive operators.
On a generalization of an approximation operator defined by A. Lupaş.
On a problem of A. Lupaş.
On a q-analogue of Stancu operators
This paper is concerned with a generalization in q-Calculus of Stancu operators. Involving modulus of continuity and Lipschitz type maximal function, we give estimates for the rate of convergence. A probabilistic approach is presented and approximation properties are established.
On a sequence of linear and positive operators.
On an approximation processes in the space of analytical functions
In this paper we obtain various approximation theorems by means of k-positive linear operators defined on the space of all analytic functions on a bounded domain of the complex plane.
On approximation by modified Bernstein polynomials.
On approximation of functions by certain operators preserving
In this paper we extend the Duman-King idea of approximation of functions by positive linear operators preserving , . Using a modification of certain operators preserving and , we introduce operators which preserve and and next we define operators for -times differentiable functions. We show that and have better approximation properties than and .
On approximation of integrable functions by modified Bernstein polynomials.
On Bernstein type operators