Global smoothness preservation and simultaneous approximation by multivariate discrete operators
Dedicated to Professor Gheorghe Coman on the occasion of his 80th anniversary
Keywords:
Simultaneous global smoothness, simultaneous approximation with rates, multivariate generalized discrete singular operators, modulus of smoothness.Abstract
In this article we study the multivariate generalized discrete singular operators defined on R N , N ≥ 1, regarding their simultaneus global smoothness preservation property with respect to Lp norm for 1 ≤ p ≤ ∞, by using higher order moduli of smoothness. Furthermore, we study their simultaneous approximation properties.
Mathematics Subject Classification (2010): 26A15, 26D15, 41A17, 41A25, 41A28, 41A35, 41A80.
References
Anastassiou, G.A., Approximation by Multivariate Singular Integrals, Briefs in Mathematics, Springer, New York, 2011.
Anastassiou, G.A., On Discrete Gauss-Weierstrass and Picard Operators, Panamer. Math. J., 23(2013), no. 2, 79{86.
Anastassiou, G.A., Kester, M., Global Smoothness and Approximation by Generalized Discrete Singular Operators, Rev. Anal. Numer. Theor. Approx., 43(2014), no. 2, 113-140.
Anastassiou, G.A., Kester, M., Approximation with Rates by Multivariate Generalized Discrete Singular Operators, AMAT 2015 Proceedings, Springer, NY, 2016, Accepted for publication.
Anastassiou, G.A., Kester, M., Lp Approximation with Rates by Multivariate Generalized Discrete Singular Operators, Applied Mathematics and Computation, 265(2015), 652-666.
Anastassiou, G.A., Kester, M., Voronovskaya Type Asymptotic Expansions for Multi-variate Generalized Discrete Singular Operators, AMAT 2015 Proceedings, Springer, NY, 2016, Accepted for publication.
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