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Existence of Solutions to a Generalized System

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Abstract

In this paper, we consider a generalized system in real Banach spaces. Using Brouwer’s fixed-point theorem, we establish some existence theorems for generalized system without monotonicity. Further, we extend the concept of C-strong pseudomonotonicity for a bifunction and extend Minty’s lemma for a generalized system. Furthermore, using the Minty lemma and KKM-Fan lemma, we establish an existence theorem for a generalized system with monotonicity in real reflexive Banach spaces.

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Authors and Affiliations

  1. Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India

    K. R. Kazmi & S. A. Khan

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  1. K. R. Kazmi
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  2. S. A. Khan
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Correspondence to K. R. Kazmi.

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Communicated by F. Giannessi.

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Kazmi, K.R., Khan, S.A. Existence of Solutions to a Generalized System. J Optim Theory Appl 142, 355–361 (2009). https://doi.org/10.1007/s10957-009-9530-7

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  • DOI: https://doi.org/10.1007/s10957-009-9530-7

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