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Existence of Solutions to a Generalized System

Author

Listed:
  • K. R. Kazmi

    (Aligarh Muslim University)

  • S. A. Khan

    (Aligarh Muslim University)

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.

Suggested Citation

  • K. R. Kazmi & S. A. Khan, 2009. "Existence of Solutions to a Generalized System," Journal of Optimization Theory and Applications, Springer, vol. 142(2), pages 355-361, August.
    • Handle: RePEc:spr:joptap:v:142:y:2009:i:2:d:10.1007_s10957-009-9530-7
    DOI: 10.1007/s10957-009-9530-7
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    References listed on IDEAS

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    1. B. Djafari. Rouhani & E. Tarafdar & P. J. Watson, 2005. "Existence of Solutions to Some Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 126(1), pages 97-107, July.
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    Cited by:

    1. Suhel Ahmad Khan & Naeem Ahmad, 2013. "Existence Results for Vector Mixed Quasi-Complementarity Problems," Journal of Mathematics, Hindawi, vol. 2013, pages 1-6, February.
    2. Suhel Ahmad Khan & Jia-Wei Chen, 2015. "Gap Functions and Error Bounds for Generalized Mixed Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 767-776, September.
    3. Phan Khanh & Vo Long, 2014. "Invariant-point theorems and existence of solutions to optimization-related problems," Journal of Global Optimization, Springer, vol. 58(3), pages 545-564, March.
    4. A. P. Farajzadeh & A. Amini-Harandi & K. R. Kazmi, 2010. "Existence of Solutions to Generalized Vector Variational-Like Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 95-104, July.
    5. Pham Huu Sach, 2018. "Solution Existence in Bifunction-Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 176(1), pages 1-16, January.
    6. Gábor Kassay & Mihaela Miholca & Nguyen The Vinh, 2016. "Vector Quasi-Equilibrium Problems for the Sum of Two Multivalued Mappings," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 424-442, May.

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