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

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

Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  1. 1.Department of Mathematics, Teacher CollegeCantho UniversityCanthoVietnam
  2. 2.Department of MathematicsInternational University of Hochiminh CityHochiminh CityVietnam