Approximation with modified Phillips operators (original) (raw)

Simultaneous approximation for the Phillips operators

International Journal of Mathematics and Mathematical Sciences, 2006

We study the simultaneous approximation properties of the well-known Phillips operators. We establish the rate of convergence of the Phillips operators in simultaneous approximation by means of the decomposition technique for functions of bounded variation.

On two modified Phillips operators

Studia Universitatis Babes-Bolyai Matematica, 2019

In this note we introduce two new modified Phillips operators G 1 n and G 2 n. We obtain direct estimates for approximation of bounded continuous functions, defined on [0, ∞) by G 1 n , as well as for approximation of unbounded continuous functions by G 2 n. We improve some previous results on this topic.

Approximation Properties of Generalized Szász-Type Operators

Acta Mathematica Vietnamica, 2018

In the present paper, we study some approximation properties of the generalized Szász type operators introduced by V. Miheşan (Creat. Math. Inf. 17:466-472, 2008). We present a quantitative Voronovskaya-type theorem, local approximation theorem by means of second-order modulus of continuity and weighted approximation for these operators. The rate of convergence for differential functions whose derivatives are of bounded variation is also obtained.

Approximation of Bounded Continuous Functions by Linear Combinations of Phillips Operators

Demonstratio Mathematica, 2014

We study the approximation properties of linear combinations of the so-called Phillips operators, which can be considered as genuine Szász-Mirakjan-Durrmeyer operators. As main result, we prove a direct estimate for the rate of approximation of bounded continuous functions f E C[0,x), measured in C|\[0,x)-norm and thus generalizing the results, proved earlier by Gupta, Agrawal, and Gairola in [3]. Our estimates rely on the recent results, obtained in the joint works of M. Heilmann and the author-[10, 11]

Approximation by generalized Szasz operators involving Sheffer polynomials

arXiv (Cornell University), 2015

The purpose of this article is to give a Chlodowsky type generalization of Szász operators defined by means of the Sheffer type polynomials. We obtain convergence properties of our operators with the help of Korovkin's theorem and the order of convergence by using a classical approach, the second order modulus of continuity and Peetre's K-functional. Moreover, we study the convergence of these operators in a weighted space of functions on a positive semi-axis and estimate the approximation by using a new type of weighted modulus of continuity introduced by Gadjiev and Aral in [12]. An algorithm is also given to plot graphical examples, and we have shown the convergence of these operators towards the function and these examples can be take as a comparison between the new operators with the previous one too. Finally, some numerical examples are also given.

The approximation of bivariate Chlodowsky-Szász-Kantorovich-Charlier-type operators

Journal of inequalities and applications, 2017

In this paper, we introduce a bivariate Kantorovich variant of combination of Szász and Chlodowsky operators based on Charlier polynomials. Then, we study local approximation properties for these operators. Also, we estimate the approximation order in terms of Peetre's K-functional and partial moduli of continuity. Furthermore, we introduce the associated GBS-case (Generalized Boolean Sum) of these operators and study the degree of approximation by means of the Lipschitz class of Bögel continuous functions. Finally, we present some graphical examples to illustrate the rate of convergence of the operators under consideration.

Approximation Properties of Sz�asz Type Operators Based on Charlier Polynomials

In the present paper, we study some approximation properties of the Sz�asz type operators involving Charlier polynomials introduced by S. Varma and F. Ta�sdelen (Math. Comput. Modelling, 56 (5-6) (2012) 108-112). First, we establish approximation in a Lipschitz type space and weighted approximation theorems for these operators. Then, we obtain the error in the approximation of functions having derivatives of bounded variation.

Simultaneous approximation by a new sequence of Szãsz-beta type operators

Revista de la Unión Matemática …, 2009

In this paper, we study some direct results in simultaneous approximation for a new sequence of linear positive operators Mn(f (t); x) of Szãsz-Beta type operators. First, we establish the basic pointwise convergence theorem and then proceed to discuss the Voronovaskaja-type asymptotic formula. Finally, we obtain an error estimate in terms of modulus of continuity of the function being approximated.

On Approximation Properties of Phillips Operators Preserving Exponential Functions

Mediterranean Journal of Mathematics, 2017

In the present paper, we study a modification of the Phillips operators, which reproduces constant and the exponential functions. We obtain the moments using the concept of moment-generating function for the Phillips operators. Here we discuss a uniform convergence estimate for this modified forms. Also some direct estimates, which also involve the asymptotic-type result are established.

Approximation with Szász-Chlodowsky operators employing general-Appell polynomials

Journal of inequalities and applications, 2024

This article explores a Chlodowsky-type extension of Szász operators using the general-Appell polynomials. The convergence properties of these operators are established by employing the universal Korovkin-type property, and the order of approximation is determined using the classical modulus of continuity. Additionally, the weighted B-statistical convergence and statistically weighted B-summability properties of the operators are derived. Theoretical results are supported by numerical and graphical examples.

Approximation by a generalized Szász type operator for functions of two variables

Miskolc Mathematical Notes, 2014

In the present paper, we define a new Szász-Mirakjan type operator in exponential weighted spaces for functions of two variables having exponential growth at infinity using a method given by Jakimovski-Leviatan. This operator is a generalization of two variables of an operator defined by A. Ciupa [1]. In this study, we investigate approximation properties and also estimate the rate of convergence for this new operator.

Approximation by q-Szasz operators

This paper deals with approximating properties of the newly defined q-generalization of the Szász operators in the case q > 1. Quantitative estimates of the convergence in the polynomial weighted spaces and the Voronovskaja's theorem are given. In particular, it is proved that the rate of approximation by the q-Szász operators (q > 1) is of order q −n versus 1/n for the classical Szász-Mirakjan operators.

Approximation by a generalization of Szasz-Mirakjan type operators

Studia Universitatis Babes-Bolyai Matematica, 2020

In the present paper we propose a new generalization of Sz\'{a}sz-Mirakjan-type operators. We discuss their weighted convergence and rate of convergence via weighted modulus of continuity. We also give an asymptotic estimate through Voronovskaja type result for these operators.

Approximation by the -Szász-Mirakjan Operators

Abstract and Applied Analysis, 2012

This paper deals with approximating properties of theq-generalization of the Szász-Mirakjan operators in the case . Quantitative estimates of the convergence in the polynomial-weighted spaces and the Voronovskaja's theorem are given. In particular, it is proved that the rate of approximation by theq-Szász-Mirakjan operators ( ) is of order versus 1/nfor the classical Szász-Mirakjan operators.

Simultaneous Approximation For The Phillips-Bézier Operators

We study the simultaneous approximation properties of the Bézier variant of the well known Phillips operators and estimate the rate of convergence of the Phillips-Bézier operators in simultaneous approximation, for functions of bounded variation.