On two modified Phillips operators

Gancho Tachev;  ;

doi:10.24193/subbmath.2019.3.02

Dunkl generalization of Phillips operators and approximation in weighted spaces

Advances in Difference Equations ◽

10.1186/s13662-020-02820-9 ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

M. Mursaleen ◽

Md. Nasiruzzaman ◽

A. Kılıçman ◽

S. H. Sapar

Keyword(s):

Weighted Spaces ◽

Phillips Operators

Approximation Properties of Phillips Operators

Mathematics Without Boundaries ◽

10.1007/978-1-4939-1106-6_8 ◽

2014 ◽

pp. 221-243

Author(s):

N. K. Govil ◽

Vijay Gupta

Keyword(s):

Approximation Properties ◽

Phillips Operators

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

Advances in Difference Equations ◽

10.1186/s13662-019-2178-1 ◽

2019 ◽

Vol 2019 (1) ◽

Cited By ~ 1

Author(s):

Md. Nasiruzzaman ◽

Aiman Mukheimer ◽

M. Mursaleen

Keyword(s):

Phillips Operators

A generalized Dunkl type modifications of Phillips operators

Journal of Inequalities and Applications ◽

10.1186/s13660-018-1909-2 ◽

2018 ◽

Vol 2018 (1) ◽

Cited By ~ 8

Author(s):

M. Nasiruzzaman ◽

Nadeem Rao

Keyword(s):

Phillips Operators

Approximation by Linear Combinations of Complex Phillips Operators in Compact Disks

Results in Mathematics ◽

10.1007/s00025-014-0377-3 ◽

2014 ◽

Vol 66 (1-2) ◽

pp. 265-272 ◽

Cited By ~ 6

Author(s):

Vijay Gupta ◽

Gancho Tachev

Keyword(s):

Linear Combinations ◽

Phillips Operators ◽

Compact Disks

Approximation by Genuine Type (p, q)-Phillips Operators

Journal of Computer Science & Computational Mathematics ◽

10.20967/jcscm.2019.04.001 ◽

2019 ◽

Vol 9 (4) ◽

pp. 49-55

Author(s):

M. Gafarli ◽

I. Yüksel

Keyword(s):

Phillips Operators

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

International Journal of Mathematics Trends and Technology ◽

10.14445/22315373/ijmtt-v66i1p522 ◽

2020 ◽

Vol 66 (1) ◽

pp. 175-187

Author(s):

Ravi Kumar ◽

Nasiruzzaman Md

Keyword(s):

Dunkl Analogue ◽

Phillips Operators

Approximation of Bounded Continuous Functions by Linear Combinations of Phillips Operators

Demonstratio Mathematica ◽

10.2478/dema-2014-0053 ◽

2014 ◽

Vol 47 (3) ◽

Cited By ~ 2

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]

A Global Inverse Theorem for Combinations of Phillips Operators

Mediterranean Journal of Mathematics ◽

10.1007/s00009-015-0648-6 ◽

2015 ◽

Vol 13 (5) ◽

pp. 2709-2719 ◽

Cited By ~ 3

Author(s):

Gancho Tachev

Keyword(s):

Inverse Theorem ◽

Phillips Operators

Dunkl Generalization of Phillips Operators and Approximation in Weighted Spaces

10.20944/preprints202003.0218.v1 ◽

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.