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

作者：Anh Lam Quoc^*; Khanh Phan Quoc

来源：Journal of Global Optimization, 2007, 37(3): 449-465.

DOI：10.1007/s10898-006-9062-8

• metric spaces
• multivalued equilibrium problems
• holder properties
• variational inequalities
• fixed point and coincidence point problems
• vector optimization

Multivalued equilibrium problems in general metric spaces are considered. Uniqueness and Holder continuity of the solution are established under Holder continuity and relaxed Holder-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 <.,.>.

• 出版日期2007-3
• 单位南宁师范大学