In this article, we purpose to obtain several approximation properties of Sz\'{a}sz-Mirakjan-Kantorovich operators with shape parameter $\lambda \in\lbrack-1,1]$. We compute some preliminaries results such as moments and central for these operators. Next, derive the Korovkin type convergence theorem, estimate degree respect moduli continuity, functions belong Lipschitz-type class Peetre's $K$-f...

In the present paper, we introduce genuine q-Stancu-Bernstein–Durrmeyer operators Znq,α(f;x). We calculate moments of these operators, Znq,α(tj;x) for j=0,1,2, which follows a symmetric pattern. also second order central moment Znq,α((t−x)2;x). give Korovkin-type theorem; estimate rate convergence continuous functions. Furthermore, prove local approximation theorem in terms modulus continuity; ...

In this paper, using the concept of A -statistical convergence for double sequences, we investigate a Korovkin-type approximation theorem for sequences of positive linear operator on the space of all continuous real valued functions defined on any compact subset of the real two-dimensional space. Then we display an application which shows that our new result is stronger than its classical versi...

We present two general sequences of positive linear operators. The first is introduced by using a class of dependent random variables, and the second is a mixture between two linear operators of discrete type. Our goal is to study their statistical convergence to the approximated function. This type of convergence can replace classical results provided by Bohman-Korovkin theorem. A particular c...

Abstract In this paper, we obtain a Korovkin type approximation theorem for power series statistical convergence of functions belonging to the class produced by multivariable modulus continuity function. As an application theorem, construct non-tensor product Balázs BBH operator which does not converge in ordinary sense. Moreover, study promised properties and compute rate convergence. Finally,...

In this study, using the concept of statistical σ−convergence which is stronger than convergence and statistical convergence we prove a Korovkin-type approximation theorem for sequences of positive linear operators defined on C∗ which is the space of all 2π-periodic and continuous functions on R, the set of all real numbers. We also study the rates of statistical σ−convergence of approximating ...

In this paper, using the concept of A-statistical convergence for double sequences, we provide a Korovkin-type approximation theorem for positive linear operators on the space of all real-valued uniform continuous functions on [0,∞) × [0,∞) with the property that have a finite limit at the infinity. Then, we display an application which shows that our new result is stronger than its classical v...

In this paper, we introduce and investigate a new class of the parametric generalization Baskakov-Schurer-Szász-Stancu operators, which considerably extends well-known classical approximation operators. For present Korovkin type theorem Grüss-Voronovskaya theorem, also study rate its convergence. Moreover, derive several results are related to operators in weighted spaces. Finally, prove some s...

*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 ...