A generalization of Fan’s matching theorem

Chebbi, Souhail; Gourdel, Pascal; Hammami, Hakim

doi:10.1007/s11784-010-0022-z

Cited by 3 publications

(3 citation statements)

References 15 publications

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“…Finally, in this section, consider the following given in Chebbi et al [8]:…”

Section: Basic Results Of the Kkm Theorymentioning

confidence: 99%

“…Lemma 4.1. (Chebbi et al [8]) Let (X, Γ) be an L-space, Z a nonempty subset of X and F : Z X a KKM map with quasi-compactly closed values. Suppose that for some z ∈ Z, F (z) is quasi-compact.…”

Section: Basic Results Of the Kkm Theorymentioning

confidence: 99%

“…In the present paper, we review the recent transition from G-convex spaces to KKM spaces, and introduce a basic KKM theorem on abstract convex spaces satisfying the partial KKM principle." (15) In 2011, Abstract of Chebbi, Gourdel, and Hammami [8]: "We introduce a generalized coercivity type condition for set-valued maps defined on topological spaces endowed with a generalized convex structure and we extend Fan's matching theorem." They also stated: "It should be noticed that the L-convexity is different from the G-convexity defined by Park and Kim in [46] in 1993 which assumes in addition the following condition:…”

Section: (8)mentioning

confidence: 99%

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The rise and fall of L-spaces

PARK

2020

Advances in the Theory of Nonlinear Analysis and Its Application

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For a quite long period, the so-called L-structure or L-spaces have been studied by some authors. They have several trivial misconceptions such as their L-spaces extend the well-known generalized convex (G-convex) spaces. In order to clarify this matter and others, we show that our KKM theory on abstract convex spaces improves typical results in L-spaces. Main topics in this paper are related to extensions of the Himmelberg fixed point theorem. Since such studies are beyond of L-spaces, we cordially claim that now is the proper time to give up the useless study on L-spaces and their variants FC-spaces.

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“…Finally, in this section, consider the following given in Chebbi et al [8]:…”

Section: Basic Results Of the Kkm Theorymentioning

confidence: 99%

Section: Basic Results Of the Kkm Theorymentioning

confidence: 99%

Section: (8)mentioning

confidence: 99%

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The rise and fall of L-spaces

PARK

2020

Advances in the Theory of Nonlinear Analysis and Its Application

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Some Fundamental Topological Fixed Point Theorems for Set-Valued Maps

Ben-El-Mechaiekh¹

2013

Topics in Fixed Point Theory

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The rise and fall of L-spaces, II

Park

2021

Advances in the Theory of Nonlinear Analysis and Its Application

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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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A generalization of Fan’s matching theorem

Cited by 3 publications

References 15 publications

The rise and fall of L-spaces

The rise and fall of L-spaces

Some Fundamental Topological Fixed Point Theorems for Set-Valued Maps

The rise and fall of L-spaces, II

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