Piecewise linear approximations of set-valued maps
Journal of Approximation Theory
Extensions of Lipschitz selections and an application to differential inclusions
Nonlinear Analysis: Theory, Methods & Applications
Spline subdivision schemes for convex compact sets
Journal of Computational and Applied Mathematics - Special issue/Dedicated to Prof. Larry L. Schumaker on the occasion of his 60th birthday
On quasilinear spaces of convex bodies and intervals
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)
Solving large classes of nonlinear systems of PDEs
Computers & Mathematics with Applications
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In this paper we consider possible topological and algebraic structures on some spaces of set-valued maps. In particular, we introduce algebraic operations on the set M(X,Y) of all minimal upper semi-continuous compact-valued maps from a topological space X into a topological group Y. It is shown that, under suitable assumptions on the spaces X and Y, we may equip the set M(X,Y) with a group structure. This structure extends the usual pointwise operations on the set of point-valued continuous functions. We also introduce convergence structures on certain sets of set-valued maps. In particular, we consider the continuous convergence structure on sets of upper semi-continuous maps, as well as a convergence structure on M(X,Y) derived through it, which is compatible with the mentioned algebraic structure. It is also shown that the generalized compact-open topology is compatible with the algebraic structure introduced on M(X,Y).