Journal of Global Optimization

, Volume 37, Issue 3, pp 449–465

Uniqueness and Hölder continuity of the solution to multivalued equilibrium problems in metric spaces


    • Department of Mathematics, Teacher CollegeCantho University
  • Phan Quoc Khanh
    • Department of MathematicsInternational University of Hochiminh City
Original Paper

DOI: 10.1007/s10898-006-9062-8

Cite this article as:
Anh, L.Q. & Khanh, P.Q. J Glob Optim (2007) 37: 449. doi:10.1007/s10898-006-9062-8


Multivalued equilibrium problems in general metric spaces are considered. Uniqueness and Hölder continuity of the solution are established under Hölder continuity and relaxed Hölder-related monotonicity assumptions. The assumptions appear to be weaker and the inclusion to be properly stronger than that of the recent results in the literature. Furthermore, our theorems include completely some known results for variational inequalities in Hilbert spaces, which were demonstrated via geometrical techniques based on the orthogonal projection in Hilbert spaces and the linearity of the canonical pair \(\langle .,.\rangle\).


Metric spacesMultivalued equilibrium problemsHölder propertiesVariational inequalitiesFixed point and coincidence point problemsVector optimization
Download to read the full article text

Copyright information

© Springer Science+Business Media B.V. 2006