A generalization of Fan’s matching theorem

Chebbi, Souhail; Gourdel, Pascal; Hammami, Hakim

doi:10.1007/s11784-008-0059-4

Cited by 1 publication

(10 citation statements)

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“…In our previous work [34] in 2013, we showed that better forms of theorems in [5,7,8,9,11] can be deduced from a KKM theorem on abstract convex spaces in our sense [2327]. Moreover, in our recent work [38], we showed that our KKM theory on abstract convex spaces improves and extends all of typical results on L-spaces.…”

Section: Introductionsupporting

confidence: 54%

“…In this section, we obtain generalizations of coercing families considered by Ben-El-Mechaiekh et al [5], Chebbi-Gourdel-Hammami [11], Chebbi [8], Hammami [17], and Gourdel-Hammami [16].…”

Section: Generalizations Of Various Coercing Familiesmentioning

confidence: 99%

“…In 2011, Chebbi et al [11] introduced the notion of coercing family in L-spaces for a given map as follows:…”

Section: Generalizations Of Various Coercing Familiesmentioning

confidence: 99%

“…The following was adopted by Hammami [17] in 2007 and Gourdel-Hammami [16] in 2007, and originated from Chebbi-Gourdel-Hammami [11] in 2011:…”

Section: Generalizations Of Various Coercing Familiesmentioning

confidence: 99%

“…This type of studies also followed by Chebbi [7,9] and others. In 2011, Chebbi, Gourdel, and Hammami [11] introduced a generalized coercivity type condition for multimaps dened on topological spaces endowed with a generalized convex structure and extended Fan's KKM theorem.…”

Section: Introductionmentioning

confidence: 99%

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In 2005, Ben-El-Mechaiekh, Chebbi, and Florenzano obtained a generalization of Ky Fan's 1984 KKM theorem on the intersection of a family of closed sets on non-compact convex sets in a topological vector space. They also extended the Fan-Browder xed point theorem to multimaps on non-compact convex sets.Since then several groups of the L-space theorists introduced coercivity families and applied them to L-spaces, H-spaces, etc. In this article, we show that better forms of such works can be deduced from a general KKM theorem on abstract convex spaces in our previous works. Consequently, all of known KKM theoretic results on L-spaces related coercivity families are extended to corresponding better forms on abstract convex spaces. This article is a continuation of our [38] and a revised and extended version of [34].

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Section: Introductionsupporting

confidence: 54%

“…In this section, we obtain generalizations of coercing families considered by Ben-El-Mechaiekh et al [5], Chebbi-Gourdel-Hammami [11], Chebbi [8], Hammami [17], and Gourdel-Hammami [16].…”

Section: Generalizations Of Various Coercing Familiesmentioning

confidence: 99%

“…In 2011, Chebbi et al [11] introduced the notion of coercing family in L-spaces for a given map as follows:…”

Section: Generalizations Of Various Coercing Familiesmentioning

confidence: 99%

“…The following was adopted by Hammami [17] in 2007 and Gourdel-Hammami [16] in 2007, and originated from Chebbi-Gourdel-Hammami [11] in 2011:…”

Section: Generalizations Of Various Coercing Familiesmentioning

confidence: 99%