Quantitative theorems on linear approximation processes of convolution operators in Banach spaces

DOI10.2748/tmj/1178229498zbMath0461.41015OpenAlexW1993434581MaRDI QIDQ1152537

Toshihiko Nishishiraho

Publication date: 1981

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1178229498

zbMATH Keywords

modulus of continuityalmost convergenceconvolution operatorapproximate identitylinear approximation processmultiplier operatorhomogeneous Banach subspace

Mathematics Subject Classification ID

Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Rate of convergence, degree of approximation (41A25) Approximation by arbitrary linear expressions (41A45)

Related Items (13)

The degree of the best approximation in Banach spaces ⋮ An abstract version of the Korovkin theorem via \(\mathcal{A}\)-summation process ⋮ Quantitative type theorems in the space of locally integrable functions ⋮ Convergence of positive linear approximation processes ⋮ On a new approach in the space of measurable functions ⋮ Saturation of multiplier operators in Banach spaces ⋮ Matrix summability and positive linear operators ⋮ Statistical relative \(\mathcal{A}\)-summation process and Korovkin-type approximation theorem on modular spaces ⋮ Summation process of positive linear operators ⋮ Statistical relative \(\mathcal{A}\)-summation process for double sequences on modular spaces ⋮ \(P\)-statistical summation process of sequences of convolution operators ⋮ The principle of subordination and comparison theorems for approximation processes of Abel-bounded orthogonal expansions ⋮ $\mathcal{F-}$relative $\mathcal{A-}$summation process for double sequences and abstract Korovkin type theorems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quantitative results on almost convergence of a sequence of positive linear operators
• The approximation of continuous functions by positive linear operators
• Topics in approximation theory
• On summation processes of Fourier expansions in Banach spaces. I: Comparison theorems
• A contribution to the theory of divergent sequences
• Convergence and almost convergence of certain sequences of positive linear operators
• Positive linear operators and summability

This page was built for publication: Quantitative theorems on linear approximation processes of convolution operators in Banach spaces