On continuity and compactness of some nonlinear operators in the spaces of functions of bounded variation

DOI10.1007/s10231-015-0526-7zbMath1362.47050OpenAlexW1875122167WikidataQ59473715 ScholiaQ59473715MaRDI QIDQ325935

Jacek Gulgowski, Dariusz Bugajewski, Piotr Kasprzak

Publication date: 11 October 2016

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10231-015-0526-7

zbMATH Keywords

Bernstein polynomialsmodulus of continuitypositive solutioncompact operatorHammerstein integral equation\(\phi\)-functionlinear integral operator\(p\)-variationVolterra-Hammerstein integral equation\(\phi\)-variation\(R_\delta\)-setacting conditionAronszajn-type theoremautonomous (nonautonomous) superposition operatorlocally bounded mappingvariation in the sense of Jordan

Mathematics Subject Classification ID

Particular nonlinear operators (superposition, Hammerstein, Nemytski?, Uryson, etc.) (47H30) Volterra integral equations (45D05) Functions of bounded variation, generalizations (26A45)

Related Items (12)

On the continuity of superposition operators in the space of functions of bounded variation ⋮ On some nonlinear operators in \(\Lambda BV\)-spaces ⋮ Types of convergence which preserve continuity ⋮ On integral operators and nonlinear integral equations in the spaces of functions of bounded variation ⋮ Unnamed Item ⋮ On the characterization of compactness in the space of functions of bounded variation in the sense of Jordan ⋮ Characterization of compact linear integral operators in the space of functions of bounded variation ⋮ The superposition operator in the space of functions continuous and converging at infinity on the real half-axis ⋮ Uniform continuity of nonautonomous superposition operators in \(\Lambda\)BV-spaces ⋮ On integral bounded variation ⋮ On \(\Lambda_p BV\)-solutions of some nonlinear integral equations on the plane ⋮ Hardy’s inequalities, Hilbert inequalities and fractional integrals on function spaces of $q$-integral $p$-variation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlinear total variation based noise removal algorithms
• Nonautonomous superposition operators in the spaces of functions of bounded variation
• Orlicz spaces and modular spaces
• Extension of uniformly continuous transformations and hyperconvex metric spaces
• On some propertis of functions of generalized variation
• On the uniform modulus of continuity of certain discrete approximation operators
• Constant rate harvesting of populations governed by Volterra integral equations
• On maps of bounded \(p\)-variation with \(p>1\)
• On BV-solutions of some nonlinear integral equations
• On mappings of higher order and their applications to nonlinear equations
• Leggett-Williams type theorems with applications to nonlinear differential and integral equations
• Image recovery using functions of bounded variation and Sobolev spaces of negative differentiability
• Topological degree and nonlinear mappings of analytic type in Banach spaces
• Helly's selection principle for functions of bounded \(p\)-variation
• On generalized variations (I)
• Deblurring Images
• Bounded Variation and Around
• On convergence of Fourier series of functions of generalized bounded variation
• Image Processing and Analysis
• Sobolev Spaces
• Convergence in Variation and Related Topics
• On a nonlinear Volterra equation

This page was built for publication: On continuity and compactness of some nonlinear operators in the spaces of functions of bounded variation