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Attempts to Approximate a Set-Valued Mapping
Given a multi-valued mapping F, we address the problem of finding another multi-valued mapping H that agrees locally with F in some sense. We show that, contrary to the scalar case, introducing a derivative of F is hardly convenient. For the case when F is convex-compact-valued, we give some possible approximations, and at the same time we show their ...
Demyanov, V.F., Lemarechal, C., Zowe, J.
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On Subdifferentials of Set-Valued Maps
Journal of Optimization Theory and Applications, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Baier, J., Jahn, J.
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Weak Subdifferentials for Set-Valued Mappings
Journal of Optimization Theory and Applications, 2013The authors investigate the weak subdifferential for set-valued mappings, which was originally introduced by \textit{G. Y. Chen} and \textit{J. Jahn} [Math. Methods Oper. Res. 48, No. 2, 187--200 (1998; Zbl 0927.90095)]. After giving some preliminaries in Section 2, two existence theorems of weak subgradients for set-valued mappings are proven in ...
Xian-Jun Long, J. W. Peng, Xiao-Bing Li
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Minimax Theorems for Set-Valued Mappings
Journal of Optimization Theory and Applications, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Li, S. J., Chen, G. Y., Lee, G. M.
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2014
Chapter 9 is devoted to set-valued mappings. We study approximate fixed points of such mappings, existence of fixed points, and the convergence and stability of iterates of set-valued mappings. In particular, we consider a complete metric space of nonexpansive set-valued mappings acting on a closed and convex subset of a Banach space with a nonempty ...
Simeon Reich, Alexander J. Zaslavski
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Chapter 9 is devoted to set-valued mappings. We study approximate fixed points of such mappings, existence of fixed points, and the convergence and stability of iterates of set-valued mappings. In particular, we consider a complete metric space of nonexpansive set-valued mappings acting on a closed and convex subset of a Banach space with a nonempty ...
Simeon Reich, Alexander J. Zaslavski
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Fuzzy integrals for set-valued mappings
Fuzzy Sets and Systems, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sung Jin Cho +3 more
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On continuity of set-valued mappings
Topology and its Applications, 2022The main results concern conditions on a topological space \(Y\) under which for a topological (possibly Baire) space \(X\) every upper or lower, or upper and lower quasi-continuous nonempty compact-valued mapping \(F:X\to K(Y)\) is upper or lower semi-countinuous at points of a residual subset of \(X\).
Ľubica Holá +1 more
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