Variational inequalities with the duality operator in Banach spaces

Authors : Insook KİM

Pages : 78-84

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Publication Date : 2020-06-30

Article Type : Research Paper

Abstract :We study variational inequality by way of metric projection in Banach spaces. The main method is to use a topological degree theory for the class of operators of monotone type in Banach spaces. More precisely, some variational inequality associated with the duality operator is considered. As applications, the problem is discussed in the Lebesgue spaces $L^p$ and the Sobolev spaces $W^{1,2}$.
Keywords : variational inequality, operators of monotone type, degree theory