HOME > Table of Contents and Abstracts > Vol. 66, No. 2
Tohoku Mathematical Journal
SECOND SERIES VOL. 66, NO. 2
|Tohoku Math. J.|
66 (2014), 171-203
VARIATIONAL INEQUALITIES FOR PERTURBATIONS OF MAXIMAL MONOTONE OPERATORS IN REFLEXIVE BANACH SPACES
Teffera M. Asfaw and Athanassios G. Kartsatos
(Received May 17, 2012, revised May 1, 2013)
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.
Mathematics Subject Classification.
Key words and phrases.
Nonlinear, maximal monotone, pseudomonotone and strongly quasibounded operators, variational inequalities, existence problems.
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