Characterizations of reflexivity and compactness via the strong Ekeland variational principle

DOI10.1016/J.NA.2009.10.019zbMath1195.46011OpenAlexW2084438107MaRDI QIDQ844953

Tomonari Suzuki

Publication date: 5 February 2010

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.2009.10.019

zbMATH Keywords

variational principles\(\tau\)-distancereflexive Banach spacesEkeland variational principlebounded compactnessHeine-Borel propertystrong Ekeland variational principle

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10) Compact (locally compact) metric spaces (54E45) Duality and reflexivity in normed linear and Banach spaces (46B10)

Related Items (2)

Fixed points and completeness in metric and generalized metric spaces ⋮ Compactness, Optimality, and Risk

Cites Work

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• Boundedly connected sets and the distance to the intersection of two sets
• The strong Ekeland variational principle, the strong drop theorem and applications
• On the variational principle
• Several fixed point theorems concerning \(\tau\)-distance
• The strong Ekeland variational principle
• Nonconvex minimization problems
• A Characterization of Complete Metric Spaces
• Caristi's fixed point theorem and metric convexity
• Shorter Notes: A Characterization of Metric Completeness
• An Introduction to Banach Space Theory
• Generalized distance and existence theorems in complete metric spaces

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