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Existence of Solutions to a Generalized System

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DOI: 10.4236/am.2012.36077    2,955 Downloads   5,042 Views   Citations


In this paper, we introduce a generalized system (for short, GS) in real Banach spaces. Using Brouwer’s fixed point theorem, we establish some existence theorems for the generalized system without monotonicity. Further, we extend the concept of C-strong pseudomonotonicity and extend Minty’s lemma for the generalized system. And using the Minty lemma and KKM-Fan lemma, we establish an existence theorem for the generalized system with monotonicity in real reflexive Banach spaces. As the continuation of existing studies, our paper present a series of extended results based on existing corresponding results.

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The authors declare no conflicts of interest.

Cite this paper

Y. Zhao, L. Xing and J. Tao, "Existence of Solutions to a Generalized System," Applied Mathematics, Vol. 3 No. 6, 2012, pp. 511-516. doi: 10.4236/am.2012.36077.


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