On approximation of Bernstein–Chlodowsky–Gadjiev type operators that fix $e^{-2x}$

Abstractthat fix the function $e^{-2x} $ e − 2 x for $x\geq 0 $ x ≥ 0 . Then, we provide the approximation properties of these newly defined operators for different types of function spaces. In addition, we focus on the rate of convergence utilizing appropriate moduli of continuity. Then, we provide the Voronovskaya-type theorem for these new operators. Finally, in order to validate our theoretical results, we provide some numerical experiments that are produced by a MATLAB complier.

Convergence properties of generalized Lupaş-Kantorovich operators

In the present paper, we consider the Kantorovich modification of generalized Lupaş operators, whose construction depends on a continuously differentiable, increasing and unbounded function $\rho$. For these new operators we give weighted approximation, Voronovskaya type theorem, quantitative estimates for the local approximation.

ON MODIFIED MOMENT-TYPE OPERATORS

We propose a modification for moment-type operators in order to preserve the exponential function $e^{2cx}$ with $c>0$ on real axis. First, we present moment identities. Then, we prove two weighted convergence theorems. Finally, we present a Voronovskaya-type theorem for the new operators.

Approximation properties of modified Jain-Gamma operators

In the present paper, we study some approximation properties of a modified Jain-Gamma operator. Using Korovkin type theorem, we first give approximation properties of such operator. Secondly, we compute the rate of convergence of this operator by means of the modulus of continuity and we present approximation properties of weighted spaces. Finally, we obtain the Voronovskaya type theorem of this operator.

Approximation by mixed positive linear operators based on second-kind beta transform

In this paper, we consider mixed approximation operators based on second-kind beta transform using Szász–Mirakjan operators. For the proposed operators, we establish some direct results, Voronovskaya-type theorem, quantitative Voronovskaya-type theorem, Grüss–Voronovskaya-type theorem, weighted approximation and functions of bounded variation.

Certain approximation properties of Brenke polynomials using Jakimovski–Leviatan operators

In this article, we establish the approximation by Durrmeyer type Jakimovski–Leviatan operators involving the Brenke type polynomials. The positive linear operators are constructed for the Brenke polynomials, and thus approximation properties for these polynomials are obtained. The order of convergence and the weighted approximation are also considered. Finally, the Voronovskaya type theorem is demonstrated for some particular case of these polynomials.

A Parametric Generalization of the Baskakov-Schurer-Szász-Stancu Approximation Operators

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

APPROXIMATION PROPERTIES OF MODIFIED BASKAKOV GAMMA OPERATORS

In this present paper, we study an approximation properties of modified Baskakov-Gamma operator. Using Korovkin type theorem we first give approximation properties of this operator. Secondly, we compute the rate of convergence of this operator by means of the modulus of continuity and we give an approximation properties of weighted spaces. Finally, we study the Voronovskaya type theorem of this operator.

A new construction of Lupaş operators and its approximation properties

The aim of this paper is to study a new generalization of Lupaş-type operators whose construction depends on a real-valued function ρ by using two sequences $u_{m} $ u m and $v_{m}$ v m of functions. We prove that the new operators provide better weighted uniform approximation over $[0,\infty )$ [ 0 , ∞ ) . In terms of weighted moduli of smoothness, we obtain degrees of approximation associated with the function ρ. Also, we prove Voronovskaya-type theorem, quantitative estimates for the local approximation.