Tohoku Mathematical Journal

Variational inequalities for perturbations of maximal monotone operators in reflexive Banach spaces

Teffera M. Asfaw and Athanassios G. Kartsatos

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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.

Article information

Source
Tohoku Math. J. (2), Volume 66, Number 2 (2014), 171-203.

Dates
First available in Project Euclid: 9 July 2014

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1404911860

Digital Object Identifier
doi:10.2748/tmj/1404911860

Mathematical Reviews number (MathSciNet)
MR3229594

Zentralblatt MATH identifier
1318.47082

Subjects
Primary: 47H05: Monotone operators and generalizations

Keywords
Nonlinear maximal monotone pseudomonotone and strongly quasibounded operators variational inequalities existence problems

Citation

Asfaw, Teffera M.; Kartsatos, Athanassios G. Variational inequalities for perturbations of maximal monotone operators in reflexive Banach spaces. Tohoku Math. J. (2) 66 (2014), no. 2, 171--203. doi:10.2748/tmj/1404911860. https://projecteuclid.org/euclid.tmj/1404911860


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