A variant of a fixed point theorem of Browder and some applications. (English) Zbl 0999.47045

Balaj, Mircea

Math. Montisnigri 9, 5-13 (1998).

A new short proof of a fixed point theorem of M. Lassonde [C. R. Acad. Sci., Paris, Sér. I 310, 573-576 (1990; Zbl 0715.47038)] is given. This result is then used to obtain a proof of Kakutani-Fan-Glicksberg’s fixed point theorem and variations on two section theorems of K. Fan [Math. Ann. 142, 305-310 (1961; Zbl 0093.36701)] and [Math. Ann. 266, 519-537 (1984; Zbl 0532.47043)].

Reviewer: Ljubiša Kočinac (Aleksandrovac)

MSC:

47H10	Fixed-point theorems
47H04	Set-valued operators
49J35	Existence of solutions for minimax problems

Keywords:

set-valued mapping; section theorem; minimax inequality

Citations:

Zbl 0715.47038; Zbl 0093.36701; Zbl 0532.47043