Existence of Solutions to a Generalized System

Yali Zhao, Lin Xing, Jia Tao

Department of Mathematics, Bohai University, Jinzhou, China.

DOI: 10.4236/am.2012.36077                

Abstract

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.

Keywords

Generalized System; C-Strong Pseudomonotonicity; Brouwer’s Fixed Point Theorem; Hemicontinuous Mapping

Conflicts of Interest

The authors declare no conflicts of interest.

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