Maximal Elements of Condensing Preference Maps in Locally Convex Hausdorff Spaces

Ding Xie-ping

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Ding Xie-ping. Maximal Elements of Condensing Preference Maps in Locally Convex Hausdorff Spaces[J]. Applied Mathematics and Mechanics, 1991, 12(8): 693-696.

Citation:

Ding Xie-ping. Maximal Elements of Condensing Preference Maps in Locally Convex Hausdorff Spaces[J]. Applied Mathematics and Mechanics, 1991, 12(8): 693-696.

Citation:

Ding Xie-ping. Maximal Elements of Condensing Preference Maps in Locally Convex Hausdorff Spaces[J]. Applied Mathematics and Mechanics, 1991, 12(8): 693-696.

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Maximal Elements of Condensing Preference Maps in Locally Convex Hausdorff Spaces

Ding Xie-ping

Department of Mathematics, Sichuan Normal University, Chengdu

Received Date: 1990-10-31
Publish Date: 1991-08-15

Abstract

Abstract

Two existence theorems of maximal elements of condensing preference maps in locally convex Hausdorff spaces are proved which generalize the recent results of Mehta. One of them positively answers the open problem mentioned by Mehta.
- topological vector space,
- condensing preference map,
- maximal element

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References(17)

References

[1]	Aliprantis,C.D.and D.Brown,Equilibria in markets with a Riesz space of commodities,J.Math.Econom.,11(1983),189-207.
[2]	Border,K.,Fixed Point Theorems with Applications to Economics and Game Theory,Cambridge Univ.Press,London(1985).
[3]	Borglin,A.and H.Keiding,Existence of equilibrium actions and of equilibrium:A note on the new existence theorems,J.Math.Econom.,3(1976),313-316.
[4]	Gale,D.and A.Mas-Colell,An equilibrium existence theorem for a general model without ordered preferences,J.Math.Econom.,2(1975),9-15.
[5]	Gohberg,I.C.,L.S.Gol‘denstein and A.S.Markus,Investigations of some properties of bounded linear operators with their q-norms,Kisinev,Gos.Univ.Ucen.Zap.,29(1957),29-36.
[6]	Kuratowski,C.,Sur les espaces complets,Fund.Math.,15(1930),301-309.
[7]	Mehta,G..Topological Methods in Equilibrium Analysis,Univ.of Queensland,St.Lucia(1987).
[8]	Mehta,G.,Maximal elements in Banach spaces,Indian J.Pure Appl.Math.,20(1989),690-697.
[9]	Mehta,G.,Maximal elements of condensing preference maps,Applied Math.Letters,Ed.I.Ekeland.(to appear)
[10]	Petryshyn,W.V.and P.M.Fitzpatrick,A degree theory,fixed point theorems,and mapping theorems for multivalued noncompact mappings,Trans.Amer.Math.Soc.,194(1974),1-25.
[11]	Sadovskii,B.N.,Measures of noncompactness and condensing operators,Problemy Mat.Anal.Sloz.Sistem,2(1968),89-119.
[12]	Sonnenschein,H.,Demand theory without transitive preferences with applications to the theory of competitive equilibrium,Preferences,Utility and Demand,Eds.J.Chipman et al.,Harcourt,Brace Jovanovich,New York(1971).
[13]	Tarafdar,E.,On nonlinear variational inequalities,Proc.Amer.Math.Soc.,67(1977),95-98.
[14]	Toussaint,S.,On the existence of equilibriums in economies with infinitely many commodities and without ordered perferences,J.Econom.Theory,33(1984),98-115.
[15]	Tulcea,C.I.,On the equilibriums of generalized games,The Center for Math.Studies in Economics and Management Science,Paper No.699(1986).
[16]	Tulcea,C.I.,On the approximation of upper semi-continuous correspondences and the equilibriums of generalized games,J.Math.Anal.Appl.,136(1988),267-289.
[17]	Walker,M.,On the existence of maximal elements,J.Econom.Theory,16(1977),470-474.