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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On nonlinear variational inequalities


Author: E. Tarafdar
Journal: Proc. Amer. Math. Soc. 67 (1977), 95-98
MSC: Primary 47H05; Secondary 47H10
DOI: https://doi.org/10.1090/S0002-9939-1977-0467408-7
MathSciNet review: 0467408
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Abstract: In this note we have given a direct proof of the result which states that if K is a compact convex subset of a linear Hausdorff topological space E over the reals and T is a monotone and hemicontinuous (nonlinear) mapping of K into $ {E^ \ast }$, then there is a $ {u_0} \in K$ such that $ (T({u_0}),v - {u_0}) \geqslant 0$ for all $ v \in K$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0467408-7
Keywords: Variational inequality, monotone and hemicontinuous operators, fixed point theorem
Article copyright: © Copyright 1977 American Mathematical Society