In this work, we introduce new approximation operators for univariate setvalued functions with general compact images. We adapt linear approximation methods for real-valued functions by replacing linear combinations of numbers with new metric linear combinations of finite sequences of compact sets, thus obtaining ”metric analogues” operators for set-valued functions. The new metric linear combi...

There are presented two methods for approximation of generalized Urysohn type operators. The first them is the natural generalization method considered by Demkiv in [1]. convergence results given quantitative form, using certain moduli continuity. In final part there a few exemplifications discrete and integral operators and, particular, Bernstein Durrmeyer

and Applied Analysis 3 Since 1967, Durrmeyer introduced Bernstein-Durrmeyer operators, and there are many paperswhich studied theirproperties 1–7 . In 1991, Zhang studied the characterization of convergence forMn,1 f ;x with Jacobi weights. In 1992, Zhou 5 considered multivariate Bernstein-Durrmeyer operators Mn,d f ;x and obtained a characterization of convergence. In 2002, Xuan et al. studied...

In the present paper, we introduce a new type of Bernstein-Durrmeyer operators preserving linear functions in movable interval. The approximation rate for continuous and Voronovskaja?s asymptotic estimate are obtained.

In the present paper we introduce positive linear operators q−Bernstein Chlodowsky polynomials on a rectangular domain and obtain their Korovkin type approximation properties. The rate of convergence of this generalization is obtained by means of the modulus of continuity, and also by using the K-functional of Peetre. We obtain weighted approximation properties for these positive linear operato...

*Correspondence: [email protected] 1Department of Mathematics and Computer Science, Wuyi University, Wuyishan, 354300, China Full list of author information is available at the end of the article Abstract In this paper, a kind of Schurer type q-Bernstein-Kantorovich operators is introduced. The Korovkin type approximation theorem of these operators is investigated. The rates of convergence of ...

In this paper, we have introduced a Stancu generalization of the Szasz–Mirakyan–Bernstein Operators defined on space continuous functions compact interval. We given general formula for moments that operators. used Korovkin’s Theorem uniform approximation under some restrictions. obtained results rates in terms modulus continuity. Finally, gave Voronovskaya-type theorems.

In this work, using the concept of natural density, we introduce $\left(
 p,q\right) $-analogue Stancu-beta operators rough $\lambda$%
 -statistically $\rho$-Cauchy convergence on triple sequence spaces. We define
 set Bernstein Stancu beta opeators statistical limit points of
 a spaces and obtain to $\lambda-$statistical convergence
 criteria associated with set. Also,...

Abstract. Since for q > 1, the q-Bernstein polynomials Bn,q are not positive linear operators on C[0, 1], the investigation of their convergence properties turns out to be much more difficult than that in the case 0 < q < 1. In this paper, new results on the approximation of continuous functions by the q-Bernstein polynomials in the case q > 1 are presented. It is shown that if f ∈ C[0, 1] and ...

In this paper, we introduce a modified Bernstein-type operators based on two real parameters and study its various approximation properties. We derive some direct results e.g. Voronovkaja type asymptotic theorem, an estimate of error in ordinary as well Ditzian Totik modulus smoothness for functions belonging to the Lipschitz space. Further, examine rate Kirov Popova generalization these operat...