Convergence theorems for HL integrable vector-valued functions with applications

DOI10.1016/j.na.2008.02.093zbMath1177.28031OpenAlexW2037046909MaRDI QIDQ1001867

M. Kumpulainen, Seppo Heikkilä, Seppo Seikkala

Publication date: 19 February 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2008.02.093

zbMATH Keywords

ordered Banach spacedominated convergence theoremmonotone convergence theoremHL integrabilityBochner integrability

Mathematics Subject Classification ID

Functional-differential equations with impulses (34K45) Abstract integral equations, integral equations in abstract spaces (45N05) Singular nonlinear integral equations (45G05) Set functions, measures and integrals with values in ordered spaces (28B15)

Related Items (8)

Semilinear evolution equations with distributed measures ⋮ A Cauchy Problem on Time Scales with Applications ⋮ Second order initial value problems with non-absolute integrals in ordered Banach spaces ⋮ Monotone convergence theorems for Henstock-Kurzweil integrable functions and applications ⋮ Impulsive nonlocal differential equations through differential equations on time scales ⋮ Differential and integral equations with Henstock-Kurzweil integrable functions ⋮ Differential equations with non-absolutely integrable functions in ordered Banach spaces ⋮ Existence of solutions of second order boundary value problems with integral boundary conditions and singularities

Cites Work

• Controlled convergence theorem for strong variational Banach-valued multiple integrals.
• Second order three boundary value problem in Banach spaces via Henstock and Henstock-Kurzweil-Pettis integral
• Impulsive retarded differential equations in Banach spaces via Bochner-Lebesgue and Henstock integrals
• Existence theory for integrodifferential equations and Henstock-Kurzweil integral in Banach spaces
• On functional improper Volterra integral equations and impulsive differential equations in ordered Banach spaces
• On singular, functional, nonsmooth and implicit phi-Laplacian initial and boundary value problems
• On improper integrals and differential equations in ordered Banach spaces
• Linear Fredholm Integral Equations and the Integral of Kurzweil
• The monotone convergence theorem for multidimensional abstract Kurzweil vector integrals
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