Approximation Properties of a Certain Modification of Durrmeyer Operators

We study approximation properties of a new operator DM,1 n (f, x) introduced by Acu et al. in [Results Math 74:90, (2019)] for Lebesgue integrable functions in [0,1]. An error estimate by the Bezier variant of the operators DM,1 n (f, x)is also obtained for the functions of bounded variation. By relevant numerical examples, the orders of approximation by the operator DM,1 n (f, x) and the modified-Bernstein-Durrmeyer operator are also compared.

Approximation of Functions by Dunkl-Type Generalization of Szász-Durrmeyer Operators Based on p , q -Integers

In this article, our main purpose is to define the p , q -variant of Szász-Durrmeyer type operators with the help of Dunkl generalization generated by an exponential function. We estimate moments and establish some direct results of the aforementioned operators. Moreover, we establish some approximation results in weighted spaces.

Approximation Properties of p , q -Szász-Mirakjan-Durrmeyer Operators

In this article, we introduce a new Durrmeyer-type generalization of p , q -Szász-Mirakjan operators using the p , q -gamma function of the second kind. The moments and central moments are obtained. Then, the Voronovskaja-type asymptotic formula is investigated and point-wise estimates of these operators are studied. Also, some local approximation properties of these operators are investigated by means of modulus of continuity and Peetre K -functional. Finally, the rate of convergence and weighted approximation of these operators are presented.

GENUINE MODIFIED BASKAKOV-DURRMEYER OPERATORS

The present paper deals with genuine Baskakov Durrmeyer operators which have preserved certain functions. We have obtained quantitative Voronovskaya and quantitative Grüss type Voronovskaya theorems using the weighted modulus of continuity. These results include the preservation properties of the classical genuine Baskakov Durrmeyer operators.

Approximation of generalized nonlinear Urysohn operators using positive linear operators

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

Integral modification of Apostol-Genocchi operators

In this article, we consider Jain-Durrmeyer operators associated with the Apostol-Genocchi polynomials and study the approximation properties of these Durrmeyer operators. Furthermore, we examine the approximation behaviour of these operators including K-functional. We estimate the rate of convergence of the proposed operators for function in Lipschitz-type space and local approximation results by using modulus of continuity. Employing Mathematica software, to show the approximation and the absolute error graphically by varying the values of given parameters.

Convergence of modified Szász-Mirakyan-Durrmeyer operators depending on certain parameters

<p style='text-indent:20px;'>Motivated by certain generalizations, in this paper we consider a new analogue of modified Szá sz-Mirakyan-Durrmeyer operators whose construction depends on a continuously differentiable, increasing and unbounded function <inline-formula><tex-math id="M1">\begin{document}$ \tau $\end{document}</tex-math></inline-formula> with extra parameters <inline-formula><tex-math id="M2">\begin{document}$ \mu $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M3">\begin{document}$ \lambda $\end{document}</tex-math></inline-formula>. Depending on the selection of <inline-formula><tex-math id="M4">\begin{document}$ \mu $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M5">\begin{document}$ \lambda $\end{document}</tex-math></inline-formula>, these operators are more flexible than the modified Szá sz-Mirakyan-Durrmeyer operators while retaining their approximation properties. For these operators we give weighted approximation, Voronovskaya type theorem and quantitative estimates for the local approximation.</p>