Modular convergence theorems for integral operators in the context of filter exhaustiveness and applications

DOI10.1007/s00009-012-0199-zzbMath1266.41017OpenAlexW2000330066MaRDI QIDQ1949850

Xenofon Dimitriou, Antonio Boccuto

Publication date: 17 May 2013

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00009-012-0199-z

zbMATH Keywords

integral operatormodularfilter convergencemodular convergenceMellin operatorfilter exhaustivenessfilter singularityMellin-Gauss-Weierstrass operatorMellin-Poisson-Cauchy operatormoment operator

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 (11)

Korovkin-type theorems for abstract modular convergence ⋮ Some applications of modular convergence in vector lattice setting ⋮ Abstract Korovkin-type theorems in modular spaces and applications ⋮ Triangular \(A\)-statistical approximation by double sequences of positive linear operators ⋮ Convergence Results for Nonlinear Sampling Kantorovich Operators in Modular Spaces ⋮ Convergence of perturbed sampling Kantorovich operators in modular spaces ⋮ Filter convergence and decompositions for vector lattice-valued measures ⋮ 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 ⋮ Convergence of sampling Kantorovich operators in modular spaces with applications ⋮ Abstract integration with respect to measures and applications to modular convergence in vector lattice setting

Cites Work

• A note on the Voronovskaja theorem for Mellin-Fejér convolution operators
• Orlicz spaces and modular spaces
• A direct approach to the Mellin transform
• Modular filter convergence theorems for Urysohn integral operators and applications
• The integrals in Gradshteyn and Ryzhik. Part 6: the beta function
• Brooks-Jewett-type theorems for the pointwise ideal convergence of measures with values in (l)-groups
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