Concepts of lower semicontinuity and continuous selections for convex valued multifunctions

DOI10.1016/0021-9045(92)90105-WzbMath0754.41037MaRDI QIDQ1185260

Longin E. Rybiński, Krzysztof Przeslawski

Publication date: 28 June 1992

Published in: Journal of Approximation Theory (Search for Journal in Brave)

zbMATH Keywords

continuous selectionsmultivalued mappingsset valued mapsMichael selection theoremgraphs of selections

Mathematics Subject Classification ID

Set-valued maps in general topology (54C60) Selections in general topology (54C65) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Related Items (13)

Barycentric selectors and a Steiner-type point of a convex body in a Banach space ⋮ Bicommutants of multiplication operators ⋮ Michael selection problem in hyperconvex metric spaces ⋮ A comparative study of various notions of approximation of sets ⋮ Michael's selection theorem under an assumption weaker than lower semicontinuous in \(H\)-spaces ⋮ On fixed point and almost fixed point problems of lower semicontinuous type multivalued mappings ⋮ On fixed point and almost fixed point problems of lower semicontinuous type multivalued mappings ⋮ On Maximal Element Problem and Quasi-Variational Inequality Problem in L.C. Metric Spaces ⋮ Continuous selections and retractive representations for the fixed points sets of set valued Reich's contractions ⋮ Continuous selections for multivalued mappings with closed convex images and applications ⋮ Nonconvexity in problems of multivalued calculus ⋮ On the core of a low dimensional set-valued mapping ⋮ Lower semicontinuity concepts, continuous selections, and set valued metric projections

Cites Work

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• Continuous selections. I
• Existence of maximal elements and equilibria in linear topological spaces
• Quasi-uniformization of hyperspaces and convergence of nets of semicontinuous multifunctions
• On a theorem of Deutsch and Kenderov
• A continuity condition for the existence of a continuous selection for a set-valued mapping
• Lower semicontinuity, almost lower semicontinuity, and continuous selections for set-valued mappings
• Set valued mappings, continuous selections, and metric projections
• A characterization of reflexive spaces by means of continuous approximate selections for metric projections
• Convex analysis and measurable multifunctions
• Various continuities of metric projections in \(C_ 0(T,X)\)
• On continuous selections for metric projections in spaces of continuous functions
• Michael Selection Theorem Under Weak Lower Semicontinuity Assumption
• Continuous Selections and Approximate Selection for Set-Valued Mappings and Applications to Metric Projections
• Continuous Selections for Weakly Hausdorff Lower Semicontinuous Multifunctions
• Theorems of Namioka and R. E. Johnson Type for Upper Semicontinuous and Compact Valued Set-Valued Mappings

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