A review of the KKM theory on φA-spaces or GFC-spaces

Sehie Park


In the KKM theory, G-convex spaces are extended to KKM spaces or abstract convex spaces in 2006. Various types of φA-spaces (X,D;{φA}A∈hDi) appeared until 2007 can be made into G-convex spaces in several ways. Moreover, various types of generalized KKM maps on φA-spaces are simply KKM maps on G-convex spaces. Therefore, our G-convex space theory can be applied to various types of φA- spaces. However, Khanh et al. in 2009 introduced a disguised form of φA-spaces called GFC-spaces. In the present paper, we review their works on GFC-spaces and clarify that their basic results are consequences of known ones. Finally, further comments on each of seven papers on GFC-spaces are given.

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How to Cite this Article:

Sehie Park, A review of the KKM theory on φA-spaces or GFC-spaces, Adv. Fixed Point Theory, 3 (2013), 355-382

Copyright © 2013 Sehie Park. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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