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2014 Variational inequalities for perturbations of maximal monotone operators in reflexive Banach spaces
Teffera M. Asfaw, Athanassios G. Kartsatos
Tohoku Math. J. (2) 66(2): 171-203 (2014). DOI: 10.2748/tmj/1404911860

Abstract

Let $X$ be a real reflexive locally uniformly convex Banach space with locally uniformly convex dual space $X^*,$ and let $K$ be a nonempty, closed and convex subset of $X$ with $0$ in its interior. Let $T$ be maximal monotone and $S$ a possibly unbounded pseudomonotone, or finitely continuous generalized pseudomonotone, or regular generalized pseudomonotone operator with domain $K$. Let $\phi$ be a proper, convex and lower semicontinuous function. New results are given concerning the solvability of perturbed variational inequalities involving the operator $T+S$ and the function $\phi$. The associated range results for nonlinear operators are also given, as well asextensions and/or improvements of known results of Kenmochi, Le, Browder, Browder and Hess, De Figueiredo, Zhou, and others.

Citation

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Teffera M. Asfaw. Athanassios G. Kartsatos. "Variational inequalities for perturbations of maximal monotone operators in reflexive Banach spaces." Tohoku Math. J. (2) 66 (2) 171 - 203, 2014. https://doi.org/10.2748/tmj/1404911860

Information

Published: 2014
First available in Project Euclid: 9 July 2014

zbMATH: 1318.47082
MathSciNet: MR3229594
Digital Object Identifier: 10.2748/tmj/1404911860

Subjects:
Primary: 47H05

Rights: Copyright © 2014 Tohoku University

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Vol.66 • No. 2 • 2014
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