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G. Tian, “Fixed Points Theorems for Mappings with Non-Compact and Non-Convex Domains,” Journal of Mathematical Analysis and Applications, Vol. 158, No. 1, 1991, pp. 161-167. doi:10.1016/0022-247X(91)90274-4

has been cited by the following article:

• TITLE: Existence of Competitive Equilibria without Standard Boundary Behavior

  AUTHORS: Francesco Ruscitti

  KEYWORDS: Excess Demand Function, Competitive Equilibrium, Set-Valued Functions, Selections, Fixed Points, Maximal Elements

  JOURNAL NAME: Applied Mathematics, Vol.2 No.11, November 30, 2011

  ABSTRACT: We study the existence of competitive equilibria when the excess demand function fails to satisfy the standard boundary behavior. We introduce alternative boundary conditions and we examine their role in proving the existence of strictly positive solutions to a system of non-linear equations (competitive equilibium prices). In addition, we slightly generalize a well-known theorem on the existence of maximal elements, and we unveil the link between the hypothesis of our theorem and one of the boundary conditions introduced in this work.