Matching theorems and simultaneous relation problems
Bull. Korean Math. Soc. 2011 Vol. 48, No. 5, 939-949
https://doi.org/10.4134/BKMS.2011.48.5.939
Printed September 1, 2011
Mircea Balaj and Lucian Coroianu
University of Oradea, University of Oradea
Abstract : In this paper we give two matching theorems of Ky Fan type concerning open or closed coverings of nonempty convex sets in a topological vector space. One of them will permit us to put in evidence, when $X$ and $Y$ are convex sets in topological vector spaces, a new subclass of $\mathbf{KKM}(X,Y)$ different by any admissible class $\frak{A}_c(X,Y)$. For this class of set-valued mappings we establish a KKM-type theorem which will be then used for obtaining existence theorems for the solutions of two types of simultaneous relation problems.
Keywords : matching theorem, KKM theorem, $\mathbf{KKM}(X,Y)$, $\frak{A}_c(X,Y)$, variational relation
MSC numbers : 47H10, 49J53
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