Generalizations of the FKKM theorem and the Ky Fan minimax inequality, with applications to maximal elements, price equilibrium, and complementarity

Tian, Guoqiang

doi:10.1016/0022-247x(92)90030-h

Cited by 132 publications

(39 citation statements)

References 13 publications

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“…A multimap F : Z ⊸ X is said to be unionly open-valued (resp., transfer open-valued) on Z if and only if the multimap G : Z ⊸ X, defined by G(z) = X\F (z) for every z ∈ Z, is intersectionally closed-valued (resp., transfer closedvalued) on Z. See [11] and Tian [15].…”

Section: Best Proximity Points Theorems In Normed Spacesmentioning

confidence: 99%

Generalized KKM-Type Theorems for Best Proximity Points

Kim¹

2016

Bulletin of the Korean Mathematical Society

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Section: Best Proximity Points Theorems In Normed Spacesmentioning

confidence: 99%

Generalized KKM-Type Theorems for Best Proximity Points

Kim¹

2016

Bulletin of the Korean Mathematical Society

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“…Let T : X ⊸ Y be a map defined by T (x) = T (x) for x ∈ X. Definition 2.1 ( [25]). Suppose that X is a nonempty set and Y is a topological space.…”

Section: Preliminariesmentioning

confidence: 99%

Coincidence Theorems for Noncompact ℜℭ-Maps in Abstract Convex Spaces With Applications

Yang¹,

Huang²

2012

Bulletin of the Korean Mathematical Society

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Abstract. In this paper, a coincidence theorem for a compact RC-map is proved in an abstract convex space. Several more general coincidence theorems for noncompact RC-maps are derived in abstract convex spaces. Some examples are given to illustrate our coincidence theorems. As applications, an alternative theorem concerning the existence of maximal elements, an alternative theorem concerning equilibrium problems and a minimax inequality for three functions are proved in abstract convex spaces.

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“…The basic transfer method is systematically developed in Tian (1992aTian ( , 1993, Zhou (1992, 1995), Zhou and Tian (1992), and Baye, Tian, and Zhou (1993) for studying the maximization of binary relations that may be nontotal or nontransitive and the existence of equilibrium in games that may have discontinuous or nonquasiconcave payoffs. The notion of recursive transfer continuity extends usual transfer continuity from single transfer to allowing recursive (sequential) transfers so that it turns out to be a necessary and sufficient condition for the existence of price equilibrium in economies with excess demand functions.…”

Section: Introductionmentioning

confidence: 99%

On the existence of price equilibrium in economies with excess demand functions

Tian

2016

Econ Theory Bull

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This paper provides a price equilibrium existence theorem in economies where commodities may be indivisible and aggregate excess demand functions may be discontinuous. We introduce a very weak notion of continuity, called recursive transfer lower semi-continuity, which is weaker than transfer lower semi-continuity and in turn weaker than lower semicontinuity. It is shown that the condition, together with Walras's law, guarantees the existence of price equilibrium in economies with excess demand functions. The condition is also necessary, and thus our results generalize all the existing results on the existence of price equilibrium in economies where excess demand is a function.Journal of Economic Literature Classification Number: C62, C72, D44, D61, D82.

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Generalizations of the FKKM theorem and the Ky Fan minimax inequality, with applications to maximal elements, price equilibrium, and complementarity

Cited by 132 publications

References 13 publications

Generalized KKM-Type Theorems for Best Proximity Points

Generalized KKM-Type Theorems for Best Proximity Points

Coincidence Theorems for Noncompact ℜℭ-Maps in Abstract Convex Spaces With Applications

On the existence of price equilibrium in economies with excess demand functions

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