Original Paper

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

  • Lam Quoc AnhAffiliated withDepartment of Mathematics, Teacher College, Cantho University Email author 
  • , Phan Quoc KhanhAffiliated withDepartment of Mathematics, International University of Hochiminh City

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Abstract

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 \(\langle .,.\rangle\).

Keywords

Metric spaces Multivalued equilibrium problems Hölder properties Variational inequalities Fixed point and coincidence point problems Vector optimization