The distributional Henstock-Kurzweil integral and applications

DOI10.1007/s00605-015-0853-1zbMath1362.45009OpenAlexW2208000708MaRDI QIDQ344232

Wei Liu, Guoju Ye

Publication date: 22 November 2016

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-015-0853-1

zbMATH Keywords

strong convergenceweak convergenceregular conenonlinear integral equationfixed-point theoremdistributional Henstock-Kurzweil integral

Mathematics Subject Classification ID

Other nonlinear integral equations (45G10) Integrals of Riemann, Stieltjes and Lebesgue type (26A42) Topological linear spaces of test functions, distributions and ultradistributions (46F05) Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) (46F30)

Related Items (6)

On the Darboux problem involving the distributional Henstock-Kurzweil integral ⋮ Henstock-Kurzweil vector distributions ⋮ Existence theorems for nonlinear second-order three-point boundary value problems involving the distributional Henstock-Kurzweil integral ⋮ The distributional Henstock-Kurzweil integral and applications II ⋮ Riemann-Liouville derivative over the space of integrable distributions ⋮ Unnamed Item

Cites Work

• The Perron integral in ordinary differential equations
• On \(x'=f(t,x)\) and Henstock-Kurzweil integrals
• The distributional Denjoy integral
• On Kurzweil generalized ordinary differential equations
• New integrals. Proceedings of the Henstock conference (12th summer symposium in real analysis), held in Coleraine, Northern Ireland, August 9-12, 1988
• A multidimensional analogue of the Denjoy-Perron-Henstock-Kurzweil integral
• First-order partial differential equations and Henstock-Kurzweil integrals
• The McShane and the Pettis integral of Banach space-valued functions defined on \(\mathbb{R}^m\)
• The Henstock integral and the Black-Scholes theory of derivative asset pricing
• On retarded functional differential equations and Henstock-Kurzweil integrals
• A Modern Theory of Random Variation
• Essentials of Integration Theory for Analysis
• Foundations for relativistic quantum theory. I. Feynman’s operator calculus and the Dyson conjectures
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