On nonlinear variational inequalities

Author:
E. Tarafdar

Journal:
Proc. Amer. Math. Soc. **67** (1977), 95-98

MSC:
Primary 47H05; Secondary 47H10

MathSciNet review:
0467408

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Abstract | References | Similar Articles | Additional Information

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 , then there is a such that for all .

**[1]**Felix E. Browder,*Nonlinear monotone operators and convex sets in Banach spaces*, Bull. Amer. Math. Soc.**71**(1965), 780–785. MR**0180882**, 10.1090/S0002-9904-1965-11391-X**[2]**Felix E. Browder,*The fixed point theory of multi-valued mappings in topological vector spaces*, Math. Ann.**177**(1968), 283–301. MR**0229101****[3]**Philip Hartman and Guido Stampacchia,*On some non-linear elliptic differential-functional equations*, Acta Math.**115**(1966), 271–310. MR**0206537****[4]**George J. Minty,*Monotone (nonlinear) operators in Hilbert space*, Duke Math. J.**29**(1962), 341–346. MR**0169064**

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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