Monotonicity properties and dominated best approximation problems in Orlicz spaces equipped with the \(p\)-Amemiya norm

DOI10.1016/j.jmaa.2015.07.004zbMath1321.41049OpenAlexW1253605739MaRDI QIDQ493834

Henryk Hudzik, Marek Wisła, Yun An Cui

Publication date: 4 September 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2015.07.004

zbMATH Keywords

Orlicz spaceuniform monotonicitystrict monotonicity\(p\)-Amemiya normdominated best approximation problemslower (upper) local uniform monotonicity

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Best approximation, Chebyshev systems (41A50) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Related Items (14)

On a certain class of norms in semimodular spaces and their monotonicity properties ⋮ Exposed points of Orlicz function spaces equipped with \(p\)-Amemiya norms ⋮ Smoothness, very (strongly) smoothness of Orlicz sequence spaces equipped with \(p\)-Amemiya norms ⋮ Geometric properties of \(F\)-normed Orlicz spaces ⋮ Uniform rotundity in every direction of Orlicz function spaces equipped with the \(p\)-Amemiya norm ⋮ Monotonicity properties and solvability of dominated best approximation problem in Orlicz spaces equipped with $s$-norms ⋮ Monotonicity Properties of Banach Lattices and Their Applications – a Survey ⋮ \(M\)-constants, Dominguez-Benavides coefficient, and weak fixed point property in Orlicz sequence spaces equipped with the \(p\)-Amemiya norm ⋮ Smoothness of Orlicz function spaces equipped with the \(p\)-Amemiya norm ⋮ Orlicz spaces equipped with \(s\)-norms ⋮ Local monotonicity coefficients in Orlicz sequence spaces equipped with the \(p\)-Amemiya norm ⋮ Geometry of Orlicz spaces equipped with norms generated by some lattice norms in \(\mathbb{R}^{2}\) ⋮ Exposed points of Orlicz sequence spaces equipped with \(p\)-Amemiya \((1\leq p\leq \infty)\) norms ⋮ Strict convexity of Orlicz sequence spaces equipped with \(p\)-Amemiya norms

Cites Work

• Non-squareness properties of Orlicz spaces equipped with the \(p\)-Amemiya norm
• Orlicz spaces and modular spaces
• Basic theory of \(p\)-Amemiya norm in Orlicz spaces (\(1\leq p\leq \infty\)): Extreme points and rotundity in Orlicz spaces endowed with these norms
• Monotonicity and best approximation in Banach lattices
• Strongly extreme points in Orlicz spaces equipped with the \(p\)-Amemiya norm
• Strictly and uniformly monotone Musielak-Orlicz spaces and applications to best approximation
• Monotonicity properties of Musielak-Orlicz spaces and dominated best approximation in Banach lattices
• Complemented Copies ofl1 in Orlicz Spaces
• Monotonicity and rotundity properties in Banach lattices
• Amemiya norm equals Orlicz norm in general
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