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Existence of Solutions to a Generalized System
Department of Mathematics, Bohai University, Jinzhou, China
Department of Mathematics, Bohai University, Jinzhou, China
Department of Mathematics, Bohai University, Jinzhou, China
- 1 Department of Mathematics, Bohai University, Jinzhou, China
- 2 Department of Mathematics, Bohai University, Jinzhou, China
- 3 Department of Mathematics, Bohai University, Jinzhou, China
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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.
KeywordsGeneralized SystemC-Strong PseudomonotonicityBrouwer’s Fixed Point TheoremHemicontinuous Mapping
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