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Zbl 1225.47060
Park, Sehie
New generalizations of basic theorems in the KKM theory. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 9, 3000-3010 (2011). ISSN 0362-546X

Some new KKM type theorems are stated for intersectionally closed-valued KKM maps. Section 2 deals with some history of the basic theorems and their pioneering applications due to Fan, Browder and others; Section 3 introduces the basic concepts of abstract spaces and KKM spaces. Section 4 deals with general KKM type theorems on abstract convex spaces satisfying a partial KKM principle for KKM maps having intersectionally closed values. In Section 5, the Fan type whole intersection theorem, the Fan-Browder type fixed point theorems, and maximal element theorems for abstract convex spaces having a partial KKM principle are deduced. Finally, Section 6 deals with a Fan type matching theorem, the Fan minimax inequality, and some variational inequalities on abstract convex spaces.
[Mihai Turinici (Iaşi)]

MSC 2000:: *47H04 Set-valued operators
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
58E35 Variational inequalities (global problems)
54H25 Fixed-point theorems in topological spaces

Keywords: intersectionally closed property; abstract convex space; fixed point; maximal element; variational inequality

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Zentralblatt MATH Berlin [Germany]