A constrained approximation theorem for integral functionals on L^p

2025/12/09 by Ricceri, Biagio
Mathematics · #Advanced Banach Space Theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis

paper · doi:10.48550/arxiv.2512.08347

openalex publication_date 2025/12/09 · openalex created_date 2025/12/11 · openalex updated_date 2026/07/28

Abstract

Let (T,\cal F,μ) be a σ-finite measure space, E a separable real Banach space and p≥ 1. Given a sequence of functions f, f₁, f₂,... from T× E to \bf R, under general assumptions, we prove that, for each closed hyperplane V of L^p(T,E), for each u∈ V, and for each sequence \λ_n\ converging to ∫_Tf(t,u(t))dμ, there exists a sequence \u_n\ in V converging to u and such that ∫_Tf_n(t,u_n(t))dμ=λ_n for all n large enough.

Citations

• Measurable relations

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