On nonlinear variational inequalities
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- by E. Tarafdar PDF
- Proc. Amer. Math. Soc. 67 (1977), 95-98 Request permission
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 $v \in K$.References
- Felix E. Browder, Nonlinear monotone operators and convex sets in Banach spaces, Bull. Amer. Math. Soc. 71 (1965), 780–785. MR 180882, DOI 10.1090/S0002-9904-1965-11391-X
- Felix E. Browder, The fixed point theory of multi-valued mappings in topological vector spaces, Math. Ann. 177 (1968), 283–301. MR 229101, DOI 10.1007/BF01350721
- Philip Hartman and Guido Stampacchia, On some non-linear elliptic differential-functional equations, Acta Math. 115 (1966), 271–310. MR 206537, DOI 10.1007/BF02392210
- George J. Minty, Monotone (nonlinear) operators in Hilbert space, Duke Math. J. 29 (1962), 341–346. MR 169064
Additional Information
- © Copyright 1977 American Mathematical Society
- 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