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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 301901, 6 pages
http://dx.doi.org/10.1155/2014/301901
Research Article

Generalized Equilibrium Problems Related to Ky Fan Inequalities

Department of Mathematics, University of Craiova, A. I. Cuza Street, No. 13, 200585 Craiova, Romania

Received 29 October 2013; Accepted 1 January 2014; Published 12 February 2014

Academic Editor: Chong Li

Copyright © 2014 Ionel Rovenţa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. X. Qin, L.-J. Lin, and S. M. Kang, “On a generalized Ky Fan inequality and asymptotically strict pseudocontractions in the intermediate sense,” Journal of Optimization Theory and Applications, vol. 150, no. 3, pp. 553–579, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. A. Tada and W. Takahashi, “Weak and strong convergence theorems for a nonexpansive mapping and an equilibrium problem,” Journal of Optimization Theory and Applications, vol. 133, no. 3, pp. 359–370, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. P. L. Combettes and S. A. Hirstoaga, “Equilibrium programming in Hilbert spaces,” Journal of Nonlinear and Convex Analysis, vol. 6, no. 1, pp. 117–136, 2005. View at Zentralblatt MATH · View at MathSciNet
  4. S. Takahashi and W. Takahashi, “Strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a Hilbert space,” Nonlinear Analysis. Theory, Methods & Applications, vol. 69, no. 3, pp. 1025–1033, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. M. Bianchi and S. Schaible, “Generalized monotone bifunctions and equilibrium problems,” Journal of Optimization Theory and Applications, vol. 90, no. 1, pp. 31–43, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. M. A. Noor and K. I. Noor, “On equilibrium problems,” Applied Mathematics E-Notes, vol. 4, pp. 125–132, 2004. View at Zentralblatt MATH · View at MathSciNet
  7. K. Nakajo and W. Takahashi, “Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups,” Journal of Mathematical Analysis and Applications, vol. 279, no. 2, pp. 372–379, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. W. Takahashi and M. Toyoda, “Weak convergence theorems for nonexpansive mappings and monotone mappings,” Journal of Optimization Theory and Applications, vol. 118, no. 2, pp. 417–428, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. C. P. Niculescu and I. Rovenţa, “Fan's inequality in geodesic spaces,” Applied Mathematics Letters, vol. 22, no. 10, pp. 1529–1533, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. C. P. Niculescu and I. Rovenţa, “Fan's inequality in the context of MP-convexity,” in Applied Analysis and Differential Equations, O. Cârja and I. Vrabie, Eds., pp. 267–274, World Scientific, Singapore, 2007, Proceedings of the International Conference on Applied Analysis and Differential Equations (ICAADE '07). View at Publisher · View at Google Scholar · View at MathSciNet
  11. C. P. Niculescu and I. Rovenţa, “Schauder fixed point theorem in spaces with global nonpositive curvature,” Fixed Point Theory and Applications, vol. 2008, Article ID 906727, 8 pages, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. J. M. Borwein and A. S. Lewis, Convex Analysis and Nonlinear Optimization. Theory and Examples, Springer, New York, NY, USA, 2000. View at MathSciNet