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Volume 1, Issue 3, 1 December 2017, Pages 357-365
Abstract. In this paper, we consider some equilibrium problems (or saddle point problems), in which the domains of the considered mappings are limited at some regions. These restricted regions are defined by some mappings which are called the constrained mappings in the given problems. For this reason, we introduce the concepts of constrained ordered equilibrium problems, that are useful extensions of ordered equilibrium problems and ordinary equilibrium problems. Then, by using some fixed point theorems on posets, we prove several theorems for the existence of solutions to some constrained ordered equilibrium problems. In particular, we investigate the solvability of some constrained ordered equilibrium problems in some partially ordered Banach spaces.
How to Cite this Article:
Jinlu Li, Constrained ordered equilibrium problems and applications, J. Nonlinear Var. Anal. 1 (2017), 357-365.