Abstract
In this article, we consider the solutions of the system of generalized variational inequality problems in Banach spaces. By employing the generalized projection operator, the well-known Fan's KKM theorem and Kakutani-Fan-Glicksberg fixed point theorem, we establish some new existence theorems of solutions for two classes of generalized set-valued variational inequalities in reflexive Banach spaces under some suitable conditions.
Highlights
1 Introduction Let E be a Banach space, E* be the dual space of E, and let 〈·,·〉 denotes the duality pairing of E* and E
If E is a Hilbert space and K is a nonempty, closed and convex subset of E, it is well known that the metric projection operator PK : E ® K plays an important role in nonlinear functional analysis, optimization theory, fixed point theory, nonlinear programming, game theory, variational inequality problem, and complementarity problems, etc
Related to the variational inequalities, we have the problem of finding the fixed points of the nonexpansive mappings, which is the current interest in functional analysis
Summary
Let E be a Banach space, E* be the dual space of E, and let 〈·,·〉 denotes the duality pairing of E* and E. Let K be a nonempty, closed and convex subset of a Hilbert space H and let A : K ® H be a mapping.
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