Existence of solutions to a generalized system. (English) Zbl 1178.49009

Summary: In this paper, we consider a generalized system in real Banach spaces. Using Brouwer’s fixed-point theorem, we establish some existence theorems for generalized system without monotonicity. Further, we extend the concept of \(C\)-strong pseudomonotonicity for a bifunction and extend Minty’s lemma for a generalized system. Furthermore, using Minty’s lemma and KKM-Fan lemma, we establish an existence theorem for a generalized system with monotonicity in real reflexive Banach spaces.


49J40 Variational inequalities
47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics
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