Modular filter convergence theorems for Urysohn integral operators and applications

DOI10.1007/s10114-013-1443-6zbMath1268.41018OpenAlexW2092727642MaRDI QIDQ2376642

Antonio Boccuto, Xenofon Dimitriou

Publication date: 24 June 2013

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-013-1443-6

zbMATH Keywords

integral operatormodular spacefilter convergencemodular convergenceMellin operatorfilter exhaustivenessfilter singularityEgorov filterLebesgue filter

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Integral operators (47G10) Approximation by operators (in particular, by integral operators) (41A35)

Related Items (12)

Korovkin-type theorems for abstract modular convergence ⋮ Statistical convergence and measure convergence generated by a single statistical measure ⋮ Abstract Korovkin-type theorems in modular spaces and applications ⋮ Approximation by positive linear operators in modular spaces by power series method ⋮ Triangular \(A\)-statistical approximation by double sequences of positive linear operators ⋮ L^pSpaces in vector lattices and applications ⋮ Modular convergence theorems for integral operators in the context of filter exhaustiveness and applications ⋮ Abstract Korovkin type theorems on modular spaces by $\mathscr{A}$-summability ⋮ Vitali-type theorems for filter convergence related to vector lattice-valued modulars and applications to stochastic processes ⋮ Rates of approximation for general sampling-type operators in the setting of filter convergence ⋮ Unnamed Item ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Orlicz spaces and modular spaces
• The notion of exhaustiveness and Ascoli-type theorems
• Statistical approximation by positive linear operators on modular spaces
• A general approximation result for nonlinear integral operators and applications to signal processing^*
• A general approach to the convergence theorems of generalized sampling series
• Approximation properties in abstract modular spaces for a class of general sampling-type operators

This page was built for publication: Modular filter convergence theorems for Urysohn integral operators and applications