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Dergiler / Advances in the Theory of Nonlinear Analysis and its Application / 2021 / Cilt: 5 - Sayı: 1

The rise and fall of L-spaces, II

Sehie PARK
Sayfa
7–24
Yayın Tarihi
2021-03-31
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

This article is a continuation of our \cite{38} and a revised and extended version of \cite{34}.

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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.
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Temel Bulgular & Veri:They also extended the Fan-Browder fixed point theorem to multimaps on non-compact convex sets.
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Sonuç & Katkı:This article is a continuation of our \cite{38} and a revised and extended version of \cite{34}.
🔬Tür:Araştırma Makalesi
📍Kapsam:2005 Verileri
⚙️Değişkenler:KKM theorem · Fan's 1961 · 1984 KKM theorem

Abstract

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 fixed 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 the 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 \cite{38} and a revised and extended version of \cite{34}.

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Bu Makaleye Atıf Yap

PARK, S. (2021). The rise and fall of L-spaces, II. Advances in the Theory of Nonlinear Analysis and its Application, Cilt: 5 - Sayı: 1, 7–24. https://ajindex.com/articles/729088

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Kaynakça (16)

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