Remarks on Voronovskaya's theorem.
Replicant compression coding in Besov spaces
We present here a new proof of the theorem of Birman and Solomyak on the metric entropy of the unit ball of a Besov space on a regular domain of The result is: if s - d(1/π - 1/p)+> 0, then the Kolmogorov metric entropy satisfies H(ε) ~ ε-d/s. This proof takes advantage of the representation of such spaces on wavelet type bases and extends the result to more general spaces. The lower bound is a consequence of very simple probabilistic exponential inequalities. To prove the upper bound,...
Replicant compression coding in Besov spaces
We present here a new proof of the theorem of Birman and Solomyak on the metric entropy of the unit ball of a Besov space on a regular domain of The result is: if then the Kolmogorov metric entropy satisfies . This...
Saturation theorem for the combinations of modified Beta operators in -spaces.
Sets with the Bernstein and generalized Markov properties
It is known that for determining sets Markov’s property is equivalent to Bernstein’s property. We are interested in finding a generalization of this fact for sets which are not determining. In this paper we give examples of sets which are not determining, but have the Bernstein and generalized Markov properties.
Sharp Estimates in Terms of Moduli of Smoothness for Compound Cubature Rules.
Simultaneous approximation by a class of Bernstein-Durrmeyer operators preserving linear functions
We introduce and study a one-parameter class of positive linear operators constituting a link between the well-known operators of S. N. Bernstein and their genuine Bernstein-Durrmeyer variants. Several limiting cases are considered including one relating our operators to mappings investigated earlier by Mache and Zhou. A recursion formula for the moments is proved and estimates for simultaneous approximation of derivatives are given.
Simultaneous approximation by a class of linear positive operators.
Simultaneous approximation for Szász-Mirakian quasi-interpolants
We obtain simultaneous approximation equivalence theorem for Szász-Mirakian quasi-interpolants.
Simultaneous approximation for the Phillips operators.
Simultaneous approximation for the Phillips-Bézier operators.
Simultaneous approximation in negative norms of arbitrary order
Some Applications of new Modified q-Szász–Mirakyan Operators
This paper we introducing a new sequence of positive q-integral new Modified q-Szász-Mirakyan Operators. We show that it is a weighted approximation process in the polynomial space of continuous functions defined on . Weighted statistical approximation theorem, Korovkin-type theorems for fuzzy continuous functions, an estimate for the rate of convergence and some properties are also obtained for these operators.
Some approximation properties of the Kantorovich variant of the Bleimann, Butzer and Hahn operators
For some classes of functions locally integrable in the sense of Lebesgue or Denjoy-Perron on the interval , the Kantorovich type modification of the Bleimann, Butzer and Hahn operators is considered. The rate of pointwise convergence of these operators at the Lebesgue or Lebesgue-Denjoy points of is estimated.
Some properties of generalized Szàsz type operators of two variables
Some properties of the Schurer type operators.
Statistical approximation by positive linear operators
Using A-statistical convergence, we prove a Korovkin type approximation theorem which concerns the problem of approximating a function f by means of a sequence Tₙ(f;x) of positive linear operators acting from a weighted space into a weighted space .
Statistical approximation of Baskakov and Baskakov-Kantorovich operators based on the q-integers
In the present paper we introduce and investigate weighted statistical approximation properties of a q-analogue of the Baskakov and Baskakov-Kantorovich operators. By using a weighted modulus of smoothness, we give some direct estimations for error in the case 0 < q < 1.
Statistical approximation properties of q-Baskakov-Kantorovich operators
In the present paper we introduce a q-analogue of the Baskakov-Kantorovich operators and investigate their weighted statistical approximation properties. By using a weighted modulus of smoothness, we give some direct estimations for error in case 0 < q < 1.
Statistical approximation to Bögel-type continuous and periodic functions
In this paper, considering A-statistical convergence instead of Pringsheim’s sense for double sequences, we prove a Korovkin-type approximation theorem for sequences of positive linear operators defined on the space of all real valued Bögel-type continuous and periodic functions on the whole real two-dimensional space. A strong application is also presented. Furthermore, we obtain some rates of A-statistical convergence in our approximation.