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Principles of Set-Valued Mappings
2013When a mapping \( f\,:\,X\to Y \) is represented in the element-chasing version \( f\,:\,a\mapsto b \) (where \( a\in X \) and \( b=f(a)\in Y \)), its relational diagram may be drawn as a network with three nodes and two directed edges, that is, a directed graph (or digraph for short):
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Regularity of Set-Valued Mappings
2011Let \( {M}:{E}\rightrightarrows {F} \) be a set-valued mapping defined from a Hausdorff topological vector space E into a normed space F and let \((\bar {x}, \bar{y})\) be a point in E × F.
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Fan’s inequality for set-valued maps
Nonlinear Analysis: Theory, Methods & Applications, 2001Georgiev, Pando Gr., Tanaka, Tamaki
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Mappings versus Set-Valued Functions
2012Inverse limits with upper semicontinuous bonding functions exhibit fundamental differences from inverse limits with mappings in the sense that the theorems that hold when the bonding functions in an inverse limit sequence are mappings almost always fail if the bonding functions are set-valued.
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