Generalizations of KKM theorem and applications to best approximations and fixed point theorems (Q5906496)

An H-KKM theorem is first obtained on \(H\)-spaces which generalizes simultaneously the corresponding results of \textit{C. Bardaro} and \textit{R.Ceppitelli} [J. Math. Anal. Appl. 132, No. 2, 484-490 (1988; Zbl 0667.49016)], \textit{Ky Fan} [Math. Ann. 226, 519-537 (1984; Zbl 0515.47029)] and \textit{M. Lassonde} [J. Math. Anal. Appl. 97, 151-201 (1983; Zbl 0527.47037)], and thus generalizes Fan's other result in [Math. Ann. 142, 305-310 (1961; Zbl 0093.367)] in many aspects. By applying this H-KKM theorem in a topological vector space setting, several results on best approximations and fixed point theorems are obtained which generalize the corresponding results of \textit{Ky Fan} [Math. Z. 112, 234-240 (1969; Zbl 0185.395)], \textit{S. Park} [Contemp. Math. 72, 183-191 (1988; Zbl 0672.47046)] and \textit{S. Reich} [Math. Z. 125, 17-31 (1972; Zbl 0216.173)].