Separation of Convex Sets and Best Approximation in Spaces with Asymmetric Norm

DOI10.2989/16073600409486100zbMath1082.41024OpenAlexW2047066162MaRDI QIDQ4659702

Ştefan Cobzaş

Publication date: 21 March 2005

Published in: Quaestiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2989/16073600409486100

zbMATH Keywords

Krein-Milman theoremseparation of convex setsspaces with asymmetric normduality of best approximation

Mathematics Subject Classification ID

Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) (46A16) Theorems of Hahn-Banach type; extension and lifting of functionals and operators (46A22) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Duality theory for topological vector spaces (46A20) Other (nonclassical) types of functional analysis (46S99)

Related Items (21)

Uniformly and locally convex asymmetric spaces ⋮ Continuity of a metric function and projection in asymmetric spaces ⋮ Local compactness in right bounded asymmetric normed spaces ⋮ Uniform structures in the beginning of the third millenium ⋮ On the approximation of the global extremum of a semi-Lipschitz function ⋮ The uniform boundedness theorem in asymmetric normed spaces ⋮ Completeness, precompactness and compactness in finite-dimensional asymmetrically normed lattices ⋮ Reflexivity for spaces with extended norm ⋮ Continuous selections of set-valued mappings and approximation in asymmetric and semilinear spaces ⋮ Density of the points of continuity of the metric function and projection in asymmetric spaces ⋮ Connectedness in asymmetric spaces ⋮ Kuhn-Tucker type theorems in cone and linear normed spaces ⋮ Asymmetric norms and optimal distance points in linear spaces ⋮ Computing optimal distances to Pareto sets of multi-objective optimization problems in asymmetric normed lattices ⋮ Compactness in asymmetric normed spaces ⋮ Characterizations of metrizable topological vector spaces and their asymmetric generalizations in terms of fuzzy (quasi-)norms ⋮ On the uniform boundedness theorem in fuzzy quasi-normed spaces ⋮ Compact and precompact sets in asymmetric locally convex spaces ⋮ Uniform convexity in nonsymmetric spaces ⋮ Compact convex sets in 2-dimensional asymmetric normed lattices ⋮ Continuous operators on asymmetric normed spaces

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