SOME GENERALIZATION OF MINTY'S LEMMA
Doo-Young Jung · 1999
We obtain a generalization of Behera and Panda's result on nonlinear scalar case to the vector version. 1. Introduction and preliminaries In the recent decades, there have been a great deal of developments in the theory of optimization techniques. The study of variational inequalities and complemen- tarity problems is also a part of this development because optimization problems can often be reduced to the solution of variational inequalities and complementarity problems. One of the important results of variational inequality theory is Minty's Lemma, which has interesting applications in the study of obstacles problems, conned plas- mas, ltration phenomena, free-boundary problems, plasticity and viscoplasticity phenomena, elasticity problems, stochastic optimal control problems and others. Let ; : X X ! R be the duality pairing. The classical Minty's Lemma (cf. (2) and (3)) is stated as follows: Theorem 1.1. Let X be a reexive real Banach space, K a nonempty closed convex subset of X and X be the dual of X. Let T : K ! X be a monotone operator