scholarly journals Approximation Order for Multivariate Durrmeyer Operators with Jacobi Weights

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Jianjun Wang ◽  
Chan-Yun Yang ◽  
Shukai Duan
Keyword(s):  
Equivalence Relation ◽  
Weak Type ◽  
Approximation Order ◽  
Modulus Of Smoothness ◽  
Inverse Theorem ◽  
Direct Theorem ◽  
Durrmeyer Operators ◽  
Jacobi Weights

Using the equivalence relation betweenK-functional and modulus of smoothness, we establish a strong direct theorem and an inverse theorem of weak type for multivariate Bernstein-Durrmeyer operators with Jacobi weights on a simplex in this paper. We also obtain a characterization for multivariate Bernstein-Durrmeyer operators with Jacobi weights on a simplex. The obtained results not only generalize the corresponding ones for Bernstein-Durrmeyer operators, but also give approximation order of Bernstein-Durrmeyer operators.

Constrained Approximation with Jacobi Weights

2016 ◽  
Vol 68 (1) ◽  
pp. 109-128 ◽  
Author(s):  
Kirill Kopotun ◽  
Dany Leviatan ◽  
Igor Shevchuk
Keyword(s):  
Polynomial Approximation ◽  
Spline Approximation ◽  
Modulus Of Smoothness ◽  
Jacobi Weights ◽  
Jacobi Weight ◽  
Constrained Approximation ◽  
Monotone Polynomial Approximation

AbstractIn this paper, we prove that for ℓ = 1 or 2 the rate of best ℓ- monotone polynomial approximation in the Lp norm (1 ≤ p ≤) weighted by the Jacobi weight with , is bounded by an appropriate (ℓ + 1)-st modulus of smoothness with the same weight, and that this rate cannot be bounded by the (ℓ + 2)-nd modulus. Related results on constrained weighted spline approximation and applications of our estimates are also given.

scholarly journals Some inequalities of trigonometric approximation in weighted Orlicz spaces

2016 ◽  
Vol 66 (1) ◽  
Author(s):  
Ramazan Akgün
Keyword(s):  
Orlicz Spaces ◽  
Trigonometric Approximation ◽  
Inverse Theorem ◽  
Direct Theorem

AbstractIn the present work, we proved a refined direct theorem and an exact inverse theorem of trigonometric approximation in Orlicz spaces with weights satisfying some Muckenhoupt’s

I-approximation properties of certain class of linear positive operators

2011 ◽  
Vol 48 (2) ◽  
pp. 205-219
Author(s):  
Nazim Mahmudov ◽  
Mehmet Özarslan ◽  
Pembe Sabancigil
Keyword(s):  
Modulus Of Smoothness ◽  
Positive Operators ◽  
Approximation Properties ◽  
Global Approximation ◽  
Linear Positive Operators ◽  
Durrmeyer Operators

In this paper we studyI-approximation properties of certain class of linear positive operators. The two main tools used in this paper areI-convergence and Ditzian-Totik modulus of smoothness. Furthermore, we defineq-Lupaş-Durrmeyer operators and give local and global approximation results for such operators.

scholarly journals Estimation of Approximation with Jacobi Weights by Multivariate Baskakov Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Jianjun Wang ◽  
Haifeng Guo ◽  
Jia Jing
Keyword(s):  
Upper Bound ◽  
Modulus Of Smoothness ◽  
Weighted Norm ◽  
Decomposition Technique ◽  
Baskakov Operators ◽  
Approximation Accuracy ◽  
Jacobi Weights ◽  
Jacobi Weight ◽  
Baskakov Operator ◽  
Bound Estimation

We first give the unboundedness of multivariate Baskakov operators with the normal weighted norm. By introducing new norms, using the multivariate decomposition technique and the modulus of smoothness with Jacobi weight, the upper bound estimation of multivariate Baskakov operators is obtained. The obtained results not only generalize the corresponding ones for multivariate Baskakov operators without weights, but also give the approximation accuracy with the Jacobi weights approximation.

scholarly journals Approximation Properties of Ibragimov-Gadjiev-Durrmeyer Operators on Lp (ℝ+)

2017 ◽  
Vol 50 (1) ◽  
pp. 156-174
Author(s):  
Gülsüm Ulusoy ◽  
Ali Aral
Keyword(s):  
Type Theorem ◽  
Modulus Of Smoothness ◽  
Weighted Norm ◽  
Approximation Properties ◽  
Korovkin Type Theorem ◽  
Approximation Process ◽  
Durrmeyer Operators ◽  
New Class ◽  
Positive Approximation Process ◽  
Durrmeyer Type Operators

Abstract We deal with the approximation properties of a new class of positive linear Durrmeyer type operators which offer a reconstruction of integral type operators including well known Durrmeyer operators. This reconstruction allows us to investigate approximation properties of the Durrmeyer operators at the same time. It is first shown that these operators are a positive approximation process in Lp(ℝ+) . While we are showing this property of the operators we consider the Ditzian-Totik modulus of smoothness and corresponding K-functional. Then, weighted norm convergence, whose proof is based on Korovkin type theorem on Lp(ℝ+), is given. At the end of the paper we show several examples of classical sequences that can be obtained from the Ibragimov-Gadjiev-Durrmeyer operators.

On the modification of the Szaśz–Durrmeyer operators

2016 ◽  
Vol 23 (3) ◽  
pp. 323-328 ◽  
Author(s):  
Ali Aral ◽  
Emre Deniz ◽  
Vijay Gupta
Keyword(s):  
Basis Function ◽  
Approximation Theorem ◽  
Modulus Of Smoothness ◽  
Quantitative Version ◽  
Durrmeyer Operators ◽  
Weighted Modulus Of Smoothness ◽  
Weighted Modulus ◽  
Direct Approximation

AbstractIn this paper we consider the modification of Szász–Durrmeyer operators based on the Jain basis function. Voronovskaya-type estimates of point-wise convergence along with its quantitative version based on the weighted modulus of smoothness are given. Moreover, a direct approximation theorem for the operators is proved.

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