Simultaneous Approximations in Banach Space-Valued Bochner–Lebesgue Spaces with Variable Exponent. (2nd January 2019)

• Record Type: Journal Article
• Authors: Wei, Haihua; Xu, Jingshi
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 1(2019)
• Page Start: 19
• Page End: 33
• Publication Date: 2019-01-02
• Subjects: Bochner–Lebesgue space -- simultaneous approximation -- variable exponent; 41A28 -- 41A65 -- 46G10; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1484762
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: Let( A, 𝒜, μ ) be a σ -finite positive measure space and let X be a Banach space. DenoteL p ( · ) ( A, 𝒜, X ) the X- valued Bochner–Lebesgue spaces with variable exponentp ( · ), wherep ( · ) be a μ measurable function on A and take values in[ 1, ∞ ] . We establish some N -simultaneous proximinality results ofL p ( · ) ( A, 𝒜 0, Y ) inL p ( · ) ( A, 𝒜, X ) if1 < ess inf ⁡ y ∈ A p ( y ) andess sup ⁡ y ∈ A p ( y ) < ∞, where𝒜 0 be a sub-algebra of𝒜 and Y be a nonempty locally weakly compact convex subset of X .