On set-valued mappings with starlike graphs |
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Authors: | R A Khachatryan |
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Institution: | 1.Yerevan State University,Yerevan,Armenia |
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Abstract: | The paper studies some topological properties of starlike bodies. It is proved that the boundary of a starlike body is a Lipschitz
surface. A separability theorem for starlike bodies is proved. It is shown that under some additional assumptions the starlike
property of the graph provides the local Lipschitz property of the set-valued mapping itself. It is shown that F. Clark’s
contingent and tangential cones are Boltyansky tents. On the base of these results, some lower and upper differentials for
set-valued mappings with starlike graphs are constructed. Some theorems on fixed points of set-valued mappings with starlike
values are proved. |
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Keywords: | |
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