caa a22 4500 606200606 CHVBK 20210128100944.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s00025-014-0412-4 doi (NATIONALLICENCE)springer-10.1007/s00025-014-0412-4 Quantitative Approximation by Fractional Generalized Discrete Singular Operators [Elektronische Daten] [George Anastassiou, Merve Kester] In this article, we study the fractional generalized smooth discrete singular operators on the real line, the univariate and non-univariate cases, regarding their convergence to the unit operator with fractional rates in the uniform norm. The related established inequalities involve the higher order moduli of smoothness of associated right and left Caputo fractional derivatives of engaged function. Furthermore we produce fractional Voronovskaya type results giving the fractional asymptotic expansion of the basic error of our approximation. We give applications and show that our operators are not in general positive. Springer Basel, 2014 Discrete fractional singular operators nationallicence modulus of smoothness nationallicence caputo fractional derivative nationallicence fractional approximation nationallicence fractional asymptotic expansion nationallicence Anastassiou George Department of Mathematical Sciences, The University of Memphis, 38152, Memphis, TN, USA aut Kester Merve Department of Mathematical Sciences, The University of Memphis, 38152, Memphis, TN, USA aut Results in Mathematics Springer Basel 67/3-4(2015-06-01), 281-301 1422-6383 67:3-4<281 2015 67 25 https://doi.org/10.1007/s00025-014-0412-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00025-014-0412-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Anastassiou George Department of Mathematical Sciences, The University of Memphis, 38152, Memphis, TN, USA aut NATIONALLICENCE 700 1- Kester Merve Department of Mathematical Sciences, The University of Memphis, 38152, Memphis, TN, USA aut NATIONALLICENCE 773 0- Results in Mathematics Springer Basel 67/3-4(2015-06-01), 281-301 1422-6383 67:3-4<281 2015 67 25