Lower semicontinuity, almost lower semicontinuity, and continuous selections for set-valued mappings

DOI10.1016/0021-9045(88)90023-8zbMath0653.41029OpenAlexW1982995731MaRDI QIDQ1107768

Frank Deutsch, Klaus Schnatz, V. Indumathi

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1016/0021-9045(88)90023-8

zbMATH Keywords

continuous selectionslower semicontinuitymetric projectionsalmost lower semicontinuity

Mathematics Subject Classification ID

Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Related Items (14)

A continuity condition for the existence of a continuous selection for a set-valued mapping ⋮ Continuities of metric projection and geometric consequences ⋮ Set valued mappings, continuous selections, and metric projections ⋮ Common best proximity pairs in strictly convex Banach spaces ⋮ Characterizations of continuous and Lipschitz continuous metric selections in normed linear spaces ⋮ Strong uniqueness, Lipschitz continuity, and continuous selections for metric projections in \(L_1\) ⋮ Norm-one projections onto subspaces of finite codimension in \(\ell_ 1\) and \(c_ 0\) ⋮ Concepts of lower semicontinuity and continuous selections for convex valued multifunctions ⋮ Approximate selections of almost lower semicontinuous multimaps in \(C\)-spaces ⋮ Generalized selection theorems without convexity ⋮ On approximation properties of \(l_1\)-type spaces ⋮ Various continuities of metric projections in \(C_ 0(T,X)\) ⋮ Best proximity points for relatively \(u\)-continuous mappings in Banach and hyperconvex spaces ⋮ Lower semicontinuity concepts, continuous selections, and set valued metric projections

Cites Work

• Continuous selections. I
• A remark on the lower semi-continuity of the set-valued metric projection
• On some geometric properties of suns
• Continuous selections for metric projections
• Continuous Selections and Approximate Selection for Set-Valued Mappings and Applications to Metric Projections
• Best n -Dimensional Approximation to Sets of Functions
• Spaces of Affine Continuous Functions on Simplexes
• Characterizations of the Space of Continuous Functions Over a Compact Hausdorff Space
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