Iterative Fixed Point Theorems and Their Applications to Ordered Variational Inequalities on Vector Lattices
Abstract. In this paper, we introduce the concept of order-continuity and ordered Lipschitz conditions of maps on vector lattices, and we provide some properties of order-continuous maps. Then, by applying these properties, we prove some theorems for the existence of fixed points for maps. As applications of these results, we solve some ordered variational inequalities on vector lattices.
Li, Jinlu, "Iterative Fixed Point Theorems and Their Applications to Ordered Variational Inequalities on Vector Lattices" (2016). Faculty Emeritus. 12.