Some geometric properties in modular spaces and application to fixed point theory

DOI10.1016/j.jmaa.2004.02.047zbMath1062.46011OpenAlexW2001124502MaRDI QIDQ596754

Japón Pineda, Maria A.

Publication date: 10 August 2004

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.2004.02.047

zbMATH Keywords

fixed pointasymptotically regular mappingsnonexpansive mappingsmodular spacesmappings of asymptotically nonexpansive typeuniform Kadec--Klee propertyuniform Opial condition

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) Fixed-point theorems (47H10) Geometry and structure of normed linear spaces (46B20) Modular spaces (46A80)

Related Items (5)

The \(\tau\)-fixed point property for left reversible semigroups ⋮ On fuzzy modular spaces ⋮ Some geometric properties of lacunary sequence spaces related to fixed point property ⋮ Some geometric properties of sequence spaces involving lacunary sequence ⋮ Convexity and boundedness relaxation for fixed point theorems in modular spaces

Cites Work

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• Orlicz spaces and modular spaces
• Asymptotic centers and nonexpansive mappings in conjugate Banach spaces
• Strongly extreme points in Köthe-Bochner spaces
• Opial modulus, moduli of noncompact convexity and fixed points for asymptotically regular mappings
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• Structure of the fixed point set and common fixed points of asymptotically nonexpansive mappings
• Existence and convergence for fixed points of mappings of asymptotically nonexpansive type
• Fixed Points and Iteration of a Nonexpansive Mapping in a Banach Space
• Geometric constants concerning metric fixed point theory: Finite or infinite dimensional character
• Demiclosedness principle and asymptotic behavior for asymptotically nonexpansive mappings
• An Introduction to Fixed Point Theory in Modular Function Spaces
• A Fixed Point Theorem for Asymptotically Nonexpansive Mappings
• Fixed-point theorems for asymptotically regular mappings in Orlicz function spaces
• Asymptotically nonexpansive mappings in modular function spaces

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