Abstract Convexity and Fixed Points

Ben-El-Mechaiekh, Hichem; Chebbi, Souhail; Florenzano, Monique; Llinares, Juan-Vicente

doi:10.1006/jmaa.1998.5918

Cited by 93 publications

(62 citation statements)

References 19 publications

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“…Formally, De…nition 1 (Ben- El-Mechaiekh et al, 1998) Let X be a topological space, X has an L-structure if there exists a non-empty valued correspondence ª : F(X) ! X and for all B 2 F(X), namely B = fb 0 ; b 1 ; :::; b n g; there exists a continuous function f B : ¢ n !…”

Section: A Kkm Resultsmentioning

confidence: 99%

A KKM-result and an application for binary and non-binary choice functions

Sánchez¹,

Llinares²,

Subiza³

2003

Economic Theory

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A B S T R A C TBy generalizing the classical Knaster-Kuratowski-Mazurkiewicz Theorem, we obtain a result that provides su¢cient conditions to ensure the non-emptiness of several kinds of choice functions. This result generalizes well-known results on the existence of maximal elements for binary relations (Bergstrom, 1975;Walker, 1977;Tian, 1993), on the non-emptiness of nonbinary choice functions (Nehring, 1996;Llinares and Sánchez, 1999) and on the non-emptiness of some classical solutions for tournaments (top cycle and uncovered set) on non-…nite sets.

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Section: A Kkm Resultsmentioning

confidence: 99%

A KKM-result and an application for binary and non-binary choice functions

Sánchez¹,

Llinares²,

Subiza³

2003

Economic Theory

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“…By comparing the definitions, it is clear that any convex subset of a topological vector space, any H-space introduced by Horvath [14] , any G-convex space introduced by Park and Kim [15] , and any L-convex space introduced by Ben-El-Mechaiekh et al [12] are all F C-spaces. Some examples of F C-spaces which are not L-convex spaces have been given by Example 1.1 of Ding [16] and Examples 2.1 and 2.2 of Ding [17] .…”

Section: Remark 12 By the Definition Of F C-subspaces Of Anmentioning

confidence: 99%

Systems of generalized vector quasi-variational inclusions and systems of generalized vector quasi-optimization problems in locally FC-uniform spaces

Ding

2009

Appl. Math. Mech.-Engl. Ed.

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In this paper, we introduce some new systems of generalized vector quasivariational inclusion problems and system of generalized vector ideal (resp., proper, Pareto, weak) quasi-optimization problems in locally F C-uniform spaces without convexity structure. By using the KKM type theorem and Himmelberg type fixed point theorem proposed by the author, some new existence theorems of solutions for the systems of generalized vector quasi-variational inclusion problems are proved. As to its applications, we obtain some existence results of solutions for systems of generalized vector quasi-optimization problems. Key wordsKKM type theorem, Himmelberg type fixed point theorem, system of generalized vector quasi-variational inclusions, system of generalized vector optimization problems, locally F C-uniform space Chinese Library Classification O176.3, O177.92 2000 Mathematics Subject Classification 49J27, 49J53, 91B50, 90C48 *

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“…The class B(Y, X) includes many important classes of mappings, such as A κ c (Y, X) in [24], KKM (Y, X) in [7] and A(Y, X) in [6], as proper subclasses.…”

Section: Preliminariesmentioning

confidence: 99%

Inclusion and Intersection Theorems With Applications in Equilibrium Theory in G-Convex Spaces

Balaj¹,

O’Regan²

2010

Journal of the Korean Mathematical Society

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Abstract. In this paper we obtain a very general theorem of ρ-compatibility for three multivalued mappings, one of them from the class B. More exactly, we show that given a G-convex space Y , two topological spaces X and Z, a (binary) relation ρ on 2 Z and three mappings P : X Z, Q : Y Z and T ∈ B(Y, X) satisfying a set of conditions we can find (e x, e y) ∈ X × Y such that e x ∈ T (e y) and P (e x)ρ Q(e y). Two particular cases of this general result will be then used to establish existence theorems for the solutions of some general equilibrium problems.

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Abstract Convexity and Fixed Points

Cited by 93 publications

References 19 publications

A KKM-result and an application for binary and non-binary choice functions

A KKM-result and an application for binary and non-binary choice functions

Systems of generalized vector quasi-variational inclusions and systems of generalized vector quasi-optimization problems in locally FC-uniform spaces

Inclusion and Intersection Theorems With Applications in Equilibrium Theory in G-Convex Spaces

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