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Equilibria and strict equilibria of multivalued maps on noninvariant sets

Pierre Cardaliaguet, Grzegorz Gabor, Marc Quincampoix (2003)

Annales Polonici Mathematici

This paper is concerned with existence of equilibrium of a set-valued map in a given compact subset of a finite-dimensional space. Previously known conditions ensuring existence of equilibrium imply that the set is either invariant or viable for the differential inclusion generated by the set-valued map. We obtain some equilibrium existence results with conditions which imply neither invariance nor viability of the given set. The problem of existence of strict equilibria is also discussed.

Existence of measurable selectors and parametrizations for $G_{δ}$ -valued multifunctions

V. Srivatsa (1984)

Fundamenta Mathematicae

Existence of quasicontinuous selections for the space $2^{f R}$

Ivan Kupka (1996)

Mathematica Bohemica

The paper presents new quasicontinuous selection theorem for continuous multifunctions $F X ⟶ ℝ$ with closed values, $X$ being an arbitrary topological space. It is known that for $2^{ℝ}$ with the Vietoris topology there is no continuous selection. The result presented here enables us to show that there exists a quasicontinuous and upper $〈$ lower $〉$ -semicontinuous selection for this space. Moreover, one can construct a selection whose set of points of discontinuity is nowhere dense.

Displaying 1 – 6 of 6

Equilibria and strict equilibria of multivalued maps on noninvariant sets

Existence of measurable selectors and parametrizations for $G_{δ}$ -valued multifunctions

Existence of quasicontinuous selections for the space $2^{f R}$

Extended Bochner Measurable Selectors.

Extension and Selection theorems in Topological spaces with a generalized convexity structure

Extensions and selections of maps with decomposable values

Currently displaying 1 – 6 of 6

Displaying 1 – 6 of 6

Equilibria and strict equilibria of multivalued maps on noninvariant sets

Existence of measurable selectors and parametrizations for G δ -valued multifunctions

Existence of quasicontinuous selections for the space 2 f R

Extended Bochner Measurable Selectors.

Extension and Selection theorems in Topological spaces with a generalized convexity structure

Extensions and selections of maps with decomposable values

Currently displaying 1 – 6 of 6

Existence of measurable selectors and parametrizations for $G_{δ}$ -valued multifunctions

Existence of quasicontinuous selections for the space $2^{f R}$