The topological versions of KKM theorem and Fan's matching theorem with applications
The authors consider some versions of the KKM theorem in topological spaces without linear structures. The purpose of this paper is to obtain some more general topological types of the KKM theorem and Fan's matching theorem. As applications, the authors shall utilize the main results to study the minimax problems and the existence of solutions for a class of generalized variational inequalities. The results of this paper are not only generalizations the corresponding results of \textit{Ky Fan} [Math. Ann. 266, 519-537 (1984; Zbl 0532.47043), Math. Ann. 142, 305-310 (1961; Zbl 0093.367)], \textit{S. Park} [J. Math. Anal. Appl. 141, 164-176 (1989; Zbl 0681.47028)], \textit{C. Bardaro} and \textit{R. Ceppitelli} [J. Math. Anal. Appl. 132, 484-490 (1988; Zbl 0667.49016), J. Math. Anal. Appl. 137, 46-58 (1989; Zbl 0681.49010)], \textit{R. Bielawski} [J. Math. Anal. Appl. 127, 155-171 (1987; Zbl 0638.52002)] and \textit{F. E. Browder} [Math. Ann. 174, 285-290 (1967; Zbl 0176.452)], but also contain the main results of \textit{B.-L. Lin} and \textit{M. Geraghty} [Proc. Am. Math. Soc. 91, 377-380 (1984; Zbl 0533.90095)], \textit{B.-L. Lin} and \textit{X.-C. Quan} [J. Math. Anal. Appl. 161, 587-590 (1991; Zbl 0779.49009)] and \textit{W. Wu} [Sci. Record, New Ser. 3, 229-232 (1959; Zbl 0168.413)].
KKM theorem in topological spaces without linear structures
scientific article; zbMATH DE number 482092