Oktay Duman

Statistical approximation of certain positive linear operators constructed by means of the Chan-Chyan-Srivastava polynomials

In this study, by obtaining some Korovkin type approximation results in statistical sense for certain positive linear operators constructed by means of the Chan-Chyan-Srivastava multivariable polynomials [W.-C.C. Chan, C.-J. Chyan, H.M. Srivastava, The Lagrange polynomials in several variables, Integral Transform. Spec. Funct. 12 (2001) 139-148], we show that our approximation method is stronger than the corresponding classical aspects in the approximation theory settings. Furthermore, we investigate their statistical rates by means of the modulus of continuity and the elements of the Lipschitz class.

Szász–Mirakjan type operators providing a better error estimation

Abstract In this work, giving a modification of the well-known Szasz–Mirakjan operators, we prove that the error estimation of our operators is better than that of the classical Szasz–Mirakjan operators. Furthermore, we obtain a Voronovskaya type theorem for these modified operators.

Statistical rates on the multivariate approximation theory

Statistical rates of approximations by means of positive linear operators defined on the space of multivariate continuous functions are studied. Furthermore, displaying an example, it is shown that our statistical rates are more efficient than the classical aspects in the approximation theory.

A-Statistical extension of the Korovkin type approximation theorem

In this paper, using the concept ofA-statistical convergence which is a regular (non-matrix) summability method, we obtain a general Korovkin type approximation theorem which concerns the problem of approximating a functionf by means of a sequenceLnf of positive linear operators.

Statistical fuzzy approximation by fuzzy positive linear operators

In this paper, we prove a Korovkin-type approximation theorem for fuzzy positive linear operators by using the notion of A-statistical convergence, where A is a non-negative regular summability matrix. This type of approximation enables us to obtain more powerful results than in the classical aspects of approximation theory settings. An application of this result is also given. Furthermore, we compute the rates of this statistical fuzzy convergence of the operators via the fuzzy modulus of continuity.

Statistical approximation results for Kantorovich-type operators involving some special polynomials

In this paper we introduce a general sequence of Kantorovich-type operators associated with some special polynomials and study their approximation properties. Mainly, we compute the rates of A-statistical convergence of these operators, which are observed to be stronger than that of the operators used commonly in Approximation Theory. Furthermore, we present an rth order generalization of our sequence of Kantorovich-type operators.

MKZ Type Operators Providing a Better Estimation on [1/2,1)

In the present paper, we introduce a modification of the Meyer-Konig and Zeller (MKZ) operators which preserve the test functions f0(x) = 1 and f2(x)= x2, and we show that this modification provides a better estimation than the classical MKZ operators on the interval [1/2, 1) with respect to the modulus of continuity and the Lipschitz class functionals. Furthermore, we present the r-th order generalization of our operators and study their approximation properties.

μ-Statistically Convergent Function Sequences

In the present paper we are concerned with convergence in μ-density and μ-statistical convergence of sequences of functions defined on a subset D of real numbers, where μ is a finitely additive measure. Particularly, we introduce the concepts of μ-statistical uniform convergence and μ-statistical pointwise convergence, and observe that μ-statistical uniform convergence inherits the basic properties of uniform convergence.

Rates of convergence of certain King-type operators for functions with derivative of bounded variation

In this paper, we estimate the rates of pointwise approximation of certain King-type positive linear operators for functions with derivative of bounded variation. We also extend our results to the statistical approximation process via the concept of statistical convergence.

Rates of A-statistical convergence of positive linear operators

Abstract In this paper we study the rates of A -statistical convergence of sequences of positive linear operators mapping the weighted space C ρ 1 into the weighted space B ρ 2 .