%0 Journal Article
%T Existence of Solutions to a Generalized System
%A Yali Zhao
%A Lin Xing
%A Jia Tao
%J Applied Mathematics
%P 511-516
%@ 2152-7393
%D 2012
%I Scientific Research Publishing
%R 10.4236/am.2012.36077
%X 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.
%K Generalized System
%K C-Strong Pseudomonotonicity
%K Brouwer¡¯s Fixed Point Theorem
%K Hemicontinuous Mapping
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=20074