Existence theorems on unbounded sets in Banach spaces

Hirano, Norimichi; Takahashi, Wataru

doi:10.1090/S0002-9939-1980-0587945-4

Existence theorems on unbounded sets in Banach spaces
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by Norimichi Hirano and Wataru Takahashi

Proc. Amer. Math. Soc. 80 (1980), 647-650

DOI: https://doi.org/10.1090/S0002-9939-1980-0587945-4

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Abstract:

In this paper, we give a necessary and sufficient condition under which a variational inequality defined on unbounded sets in a Banach space has a solution. Furthermore, we establish a necessary and sufficient condition under which the minimax equality on unbounded sets is true.

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