Abstract and Applied Analysis

Existence Results for Generalized Vector Equilibrium Problems with Multivalued Mappings via KKM Theory

A. P. Farajzadeh, A. Amini-Harandi, and D. O'Regan

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Abstract

We first define upper sign continuity for a set-valued mapping and then we consider two types of generalized vector equilibrium problems in topological vector spaces and provide sufficient conditions under which the solution sets are nonempty and compact. Finally, we give an application of our main results. The paper generalizes and improves results obtained by Fang and Huang in (2005).

Article information

Source
Abstr. Appl. Anal., Volume 2008 (2008), Article ID 968478, 8 pages.

Dates
First available in Project Euclid: 10 February 2009

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1234299001

Digital Object Identifier
doi:10.1155/2008/968478

Mathematical Reviews number (MathSciNet)
MR2466223

Zentralblatt MATH identifier
1157.49012

Citation

Farajzadeh, A. P.; Amini-Harandi, A.; O'Regan, D. Existence Results for Generalized Vector Equilibrium Problems with Multivalued Mappings via KKM Theory. Abstr. Appl. Anal. 2008 (2008), Article ID 968478, 8 pages. doi:10.1155/2008/968478. https://projecteuclid.org/euclid.aaa/1234299001


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References

  • Y.-P. Fang and N.-J. Huang, ``Existence results for generalized implicit vector variational inequalities with multivalued mappings,'' Indian Journal of Pure and Applied Mathematics, vol. 36, no. 11, pp. 629--640, 2005.
  • N. T. Tan, ``Quasi-variational inequalities in topological linear locally convex Hausdorff spaces,'' Mathematische Nachrichten, vol. 122, no. 1, pp. 231--245, 1985.
  • M. Kamenskii, V. Obukhovskii, and P. Zecca, Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces, vol. 7 of de Gruyter Series in Nonlinear Analysis and Applications, Walter de Gruyter, Berlin, Germany, 2001.
  • M. Bianchi and R. Pini, ``Coercivity conditions for equilibrium problems,'' Journal of Optimization Theory and Applications, vol. 124, no. 1, pp. 79--92, 2005.
  • N. Hadjisavvas, ``Continuity and maximality properties of pseudomonotone operators,'' Journal of Convex Analysis, vol. 10, no. 2, pp. 465--475, 2003.
  • H. Yin and C. Xu, ``Vector variational inequality and implicit vector complementarity problems,'' in Vector Variational Inequalities and Vector Equilibria, F. Giannessi, Ed., vol. 38 of Nonconvex Optimization and Its Applications, pp. 491--505, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000.
  • K. Fan, ``Some properties of convex sets related to fixed point theorems,'' Mathematische Annalen, vol. 266, no. 4, pp. 519--537, 1984.
  • S. Park, ``Recent results in analytical fixed point theory,'' Nonlinear Analysis: Theory, Methods & Applications, vol. 63, no. 5--7, pp. 977--986, 2005. \endthebibliography