Approximation of Phillips-operators on new parameters and via Dunkl analogue

2020 ◽  
Vol 66 (1) ◽  
pp. 175-187
Author(s):  
Ravi Kumar ◽  
Nasiruzzaman Md
Keyword(s):  
Dunkl Analogue ◽  
Phillips Operators

scholarly journals Dunkl generalization of Phillips operators and approximation in weighted spaces

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
M. Mursaleen ◽  
Md. Nasiruzzaman ◽  
A. Kılıçman ◽  
S. H. Sapar
Keyword(s):  
Weighted Spaces ◽  
Phillips Operators

scholarly journals Approximation results on Dunkl generalization of Phillips operators via q-calculus

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Md. Nasiruzzaman ◽  
Aiman Mukheimer ◽  
M. Mursaleen
Keyword(s):  
Phillips Operators

scholarly journals Approximation by Parametric Extension of Szász-Mirakjan-Kantorovich Operators Involving the Appell Polynomials

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Md. Nasiruzzaman ◽  
A. F. Aljohani
Keyword(s):  
Rate Of Convergence ◽  
Weighted Space ◽  
Modulus Of Smoothness ◽  
Linear Operators ◽  
Appell Polynomials ◽  
Global Approximation ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Dunkl Analogue ◽  
Kantorovich Operators

The purpose of this article is to introduce a Kantorovich variant of Szász-Mirakjan operators by including the Dunkl analogue involving the Appell polynomials, namely, the Szász-Mirakjan-Jakimovski-Leviatan-type positive linear operators. We study the global approximation in terms of uniform modulus of smoothness and calculate the local direct theorems of the rate of convergence with the help of Lipschitz-type maximal functions in weighted space. Furthermore, the Voronovskaja-type approximation theorems of this new operator are also presented.

scholarly journals Approximation of Bounded Continuous Functions by Linear Combinations of Phillips Operators

2014 ◽  
Vol 47 (3) ◽  
Author(s):  
Gancho Tachev
Keyword(s):  
Continuous Functions ◽  
Approximation Properties ◽  
Linear Combinations ◽  
Direct Estimate ◽  
Durrmeyer Operators ◽  
Rate Of Approximation ◽  
Phillips Operators ◽  
Bounded Continuous Functions

AbstractWe 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]

scholarly journals Dunkl Generalization of Phillips Operators and Approximation in Weighted Spaces

2020 ◽  
Author(s):  
M. Mursaleen ◽  
Md Nasiruzzaman ◽  
Adem Kilicman ◽  
Siti Hasana Sapar
Keyword(s):  
Rate Of Convergence ◽  
Error Estimation ◽  
Modulus Of Continuity ◽  
Second Order ◽  
Maximal Functions ◽  
Weighted Spaces ◽  
Phillips Operators ◽  
Convergence Results

Purpose of this article is to introduce a modification of Phillips operators on the interval $\left[ \frac{1}{2},\infty \right) $ via Dunkl generalization. This type of modification enables a better error estimation on the interval $\left[ \frac{1}{2},\infty \right) $ rather than the classical Dunkl Phillips operators on $\left[ 0,\infty \right) $. We discuss the convergence results and obtain the degrees of approximations. Furthermore, we calculate the rate of convergence by means of modulus of continuity, Lipschitz type maximal functions, Peetre's $K$-functional and second order modulus of continuity.

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