DOI QR코드

DOI QR Code

MIXED VECTOR EQUILIBRIUM-LIKE PROBLEMS IN BANACH SPACES

  • Lee, Byung-Soo (DEPARTMENT OF MATHEMATICS KYUNGSUNG UNIVERSITY) ;
  • Salahuddin, Salahuddin (DEPARTMENT OF MATHEMATICS ALIGARH MUSLIM UNIVERSITY) ;
  • Ahmad, M.K. (DEPARTMENT OF MATHEMATICS ALIGARH MUSLIM UNIVERSITY)
  • Received : 2009.06.03
  • Accepted : 2009.07.17
  • Published : 2009.12.31

Abstract

In this paper, we consider a new class of generalized mixed vector equilibrium-like problems in Banach spaces. By using Fan-KKM Theorem and Nadler's Theorem, we prove the existence theorem of solution for this class of generalized mixed vector equilibrium-like problems.

Keywords

References

  1. M. K. Ahmad and Salahuddin, Existence of solutions for generalized implicit vector variational like inequalities, Nonlinear Anal. 67 (2007), 430-441. https://doi.org/10.1016/j.na.2006.06.010
  2. C. Baiocchi and A. Capelo, Variational and Quasi-variational Inequalities: Applications to Free Boundary Problems, John Wiley and Sons, New York, 1984.
  3. L. C. Ceng, S. M. Guu and J. C. Yao, Generalized vector equilibrium-like problems without pseudomonotonicity in Banach spaces, JIA April 2007.
  4. K. Fan, A generalization of Tychonoff's fixed point theorem, Mathematische Annalen 142(1961), 305-310. https://doi.org/10.1007/BF01353421
  5. F. Giannessi, On Minty Variational Principle: In New Trends in Mathematical Programming, Kluwer Academic Publishers, Dordrecht, 1997.
  6. P. Hartman and G. Stampacchia, On some nonlinear elliptic differential function equations, Acta Math. 115 (1966), 271-310. https://doi.org/10.1007/BF02392210
  7. M. F. Khan and Salahuddin, On generalized vector variational like inequalities, Nonlinear Anal. 59 (2004), 879-889. https://doi.org/10.1016/j.na.2004.07.043
  8. D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and their Applications, Academic Press, New York, 1980.
  9. I. V. Konnov and J. C. Yao, Existence of solutions for generalized vector equilibrium problem, J. Math. Anal. Appl. 233 (1999), 328-335. https://doi.org/10.1006/jmaa.1999.6312
  10. B. S. Lee, S. S. Chang, J. S. Jung and S. J. Lee, Generalized vector version of Minty's lemma and applications, Comput. Math. Appl. 45 (2003), 647-653. https://doi.org/10.1016/S0898-1221(03)00024-5
  11. J. Li, N. J. Huang and J. K. Kim, On implicit vector equilibrium problem, J. Math. Anal. Appl. 283 (2003), 501-512. https://doi.org/10.1016/S0022-247X(03)00277-4
  12. Jr. S. B. Nadler, Multi-valued contraction mappings, Pacific J. Math. 30 (1969), 475-488. https://doi.org/10.2140/pjm.1969.30.475
  13. A. H. Siddiqi, M. F. Khan and Salahuddin, On vector variational like inequalities, Far East J. Math. Sci. Special 3 (1998), 319-329.
  14. L. C. Zeng and J. C. Yao, An existence result for generalized vector equilibrium problem with pseudomonotonicity, Appl. Math. Lett. 19 (2006), 1320-1326. https://doi.org/10.1016/j.aml.2005.09.010
  15. Y. Zhao and Z. Zia, On the existence of solutions to generalized vector variational-like inequalities, Nonlinear Anal. 64 (2006), 2075-2083. https://doi.org/10.1016/j.na.2005.08.003