- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 4 Issue: 3
- The rise and fall of L-spaces
The rise and fall of L-spaces
Authors : Sehie Park
Pages : 152-166
Doi:10.31197/atnaa.786151
View : 7 | Download : 3
Publication Date : 2020-08-31
Article Type : Research
Abstract :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.Keywords : FC-space, L-space, Fixed Point Theorem, (Partial) KKM space, Abstract convex space, KKM theorem, Multimap classes KC, KO