Approximation properties of weighted Kantorovich type operators in compact disks (original) (raw)

Approximation Theorems for Generalized Complex Kantorovich-Type Operators

Journal of Applied Mathematics, 2012

The order of simultaneous approximation and Voronovskaja-type results with quantitative estimate for complex q-Kantorovich polynomials q > 0 attached to analytic functions on compact disks are obtained. In particular, it is proved that for functions analytic in {z ∈ C : |z| < R}, R > q, the rate of approximation by the q-Kantorovich operators q > 1 is of order q −n versus 1/n for the classical Kantorovich operators.

Approximation by Complex Baskakov-Szász-Durrmeyer Operators in Compact Disks

Analysis in Theory and Applications

In the present paper, we deal with the complex Baskakov-Szász-Durrmeyer mixed operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth in DR = {z ∈ C; |z| < R}. Also, the exact order of approximation is found. The method used allows to construct complex Szász-type and Baskakov-type approximation operators without to involve the values on [0, ∞).

Approximation by generalized complex Szasz-Mirakyan operators in compact disk

TURKISH JOURNAL OF MATHEMATICS

In this study, the generalized complex Szász-Mirakyan operators are introduced and the approximation properties of these operators are studied. Voronovskaya's theorem with a quantitative estimate for these operators attached to an analytic function is achieved on compact disks.

Approximation by complex Szasz-Durrmeyer-Chlodowsky operators in compact disks

2016

In the present article, we deal with the overconvergence of the Sz?asz-Durrmeyer-Chlodowsky operators. Here we study the approximation properties e.g. upper estimates, Voronovskaja type result for these operators attached to analytic functions in compact disks. Also, we discuss the exact order in simultaneous approximation by these operators and its derivatives and the asymptotic result with quantitative upper estimate. In such a way, we put in evidence the overconvergence phenomenon for the Sz?asz-Durrmeyer-Chlodowsky operators, namely the extensions of approximation properties with exact quantitative estimates and orders of these convergencies to sets in the complex plane that contain the interval [0,\infty).

Approximation by generalized complex Szász–Mirakyan operators in compact disks

TURKISH JOURNAL OF MATHEMATICS, 2019

In this study, the generalized complex Szász-Mirakyan operators are introduced and the approximation properties of these operators are studied. Voronovskaya's theorem with a quantitative estimate for these operators attached to an analytic function is achieved on compact disks.

On Approximation Properties of Two Variables of Modified Kantorovich-Type Operators

Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics

In the present paper, we introduce certain modi…cation of Szász-Mirakyan-Kantorovich-type operators in polynomial weighted spaces of continuous functions of two variables. Then we research some approximation properties of these operators. We give some inequalities for the operators by means of the weighted modulus of continuity and also obtain a Voronovskaya-type theorem. Furthermore, in the paper we show that our operators give better degree of approximation of functions belonging to weighted spaces than classical Szász-Mirakyan operators.

Approximation properties of complex q-Balázs-Szabados operators in compact disks

Journal of Inequalities and Applications, 2013

This paper deals with approximating properties and convergence results of the complex q-Balázs-Szabados operators attached to analytic functions on compact disks. The order of convergence and the Voronovskaja-type theorem with quantitative estimate of these operators and the exact degree of their approximation are given. Our study extends the approximation properties of the complex q-Balázs-Szabados operators from real intervals to compact disks in the complex plane with quantitative estimate. MSC: 30E10; 41A25

Approximation by complex Chlodowsky-Szasz-Durrmeyer operators in compact disks

2020

This paper presents a study on the approximation properties of the operators constructed by the composition of Chlodowsky operators and Szasz-Durrmeyer operators. We give the approximation properties and obtain a Voronovskaya-type result for these operators for analytic functions of exponential growth on compact disks. Furthermore, a numerical example with an illustrative graphic is given to compare for the error estimates of the operators.