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L. E. J. Brouwer, “Zur Invarianz des n-Dimensional Ge- bietes,” Mathematische Annalen, Vol. 72, 1912, pp. 55-56. doi:10.1007/BF01456889

has been cited by the following article:

• TITLE: Existence of Solutions to a Generalized System

  AUTHORS: Yali Zhao, Lin Xing, Jia Tao

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

  JOURNAL NAME: Applied Mathematics, Vol.3 No.6, June 21, 2012

  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.