Approximation on variable exponent spaces by linear integral operators

This paper aims at approximation of functions by linear integral operators on variable exponent spaces associated with a general exponent function on a domain of a Euclidean space. Under a log-Hölder continuity assumption of the exponent function, we present quantitative estimates for the approximat...

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Veröffentlicht in:Journal of approximation theory Jg. 223; S. 29 - 51
Hauptverfasser: Li, Bing-Zheng, He, Bo-Lu, Zhou, Ding-Xuan
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 01.11.2017
Schlagworte:
[formula omitted]-functional
Bernstein type operators
Integral operators
Learning theory
log-Hölder continuity
Variable exponent space
Integral operators
41A36
log-Hölder continuity
68T05
K-functional
Variable exponent space
Bernstein type operators
Learning theory
68Q32
ISSN:0021-9045, 1096-0430
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Zusammenfassung:This paper aims at approximation of functions by linear integral operators on variable exponent spaces associated with a general exponent function on a domain of a Euclidean space. Under a log-Hölder continuity assumption of the exponent function, we present quantitative estimates for the approximation and solve an open problem raised in our earlier work. As applications of our key estimates, we provide high orders of approximation by quasi-interpolation type and linear combinations of Bernstein type integral operators on variable exponent spaces. We also introduce K-functionals and moduli of smoothness on variable exponent spaces and discuss their relationships and applications.
ISSN:0021-9045
1096-0430
DOI:10.1016/j.jat.2017.07.009