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Zbl 1178.49009
Kazmi, K.R.; Khan, S.A.
Existence of solutions to a generalized system. (English)
[J] J. Optim. Theory Appl. 142, No. 2, 355-361 (2009). ISSN 0022-3239; ISSN 1573-2878/e

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.

MSC 2000:: *49J40 Variational methods including variational inequalities
47N10 Appl. of operator theory in optimization, math. programming, etc.

Keywords: generalized system; strong pseudomonotone mapping; hemicontinuous mapping

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