Recent results in analytical fixed point theory

Abstract

We survey recent results in analytical fixed point theory. Firstly, we state resolutions of long-standing problems in infinite dimensional topology—the Schauder conjecture, the compact AR problem, and the Banach problem on the Hilbert cube. Secondly, we list some fixed point theorems on Kakutani maps, generalized upper hemicontinuous maps, Fan–Browder maps, approximable maps, acyclic maps, and admissible or better admissible class B of maps. Some related results are also given.