Continuity of fixed points

Continuity properties and sensitivity analysis of parameterized fixed points and approximate fixed points

In this paper we consider continuity of the set of fixed points and approximate fixed points for parameterized set-valued mappings. Continuity properties are provided for the fixed points of general multivalued mappings, with additional results shown for contraction mappings. Further analysis is provided for the continuity of the approximate fixed points of set-valued functions. Additional resu...

Automatic Continuity of Homomorphisms and Fixed Points on Metric Compacta

We prove that arbitrary homomorphisms from one of the groups Homeo(2), Homeo(2), Aut(Q, <), Homeo(R) or Homeo(S) into a separable group are automatically continuous. This has consequences for the representations of these groups as discrete groups. For example, it follows, in combination with a result of V. G. Pestov, that any action of the discrete group Homeo+(R) by homeomorphisms on a compact...

Approximating fixed points of generalized nonexpansive mappings

Diagonal arguments and fixed points

‎A universal schema for diagonalization was popularized by N.S‎. ‎Yanofsky (2003)‎, ‎based on a pioneering work of F.W‎. ‎Lawvere (1969)‎, ‎in which the existence of a (diagonolized-out and contradictory) object implies the existence of a fixed-point for a certain function‎. ‎It was shown that many self-referential paradoxes and diagonally proved theorems can fit in that schema‎. ‎Here‎, ‎we fi...

Common Fixed Points of Conditionally Commuting Mappings Satisfying Weaker Continuity Conditions

The aim of the present paper is to obtain some new common fixed point theorems for a pair of Lipschitzian type selfmappings satisfying a minimal commutativity and weaker continuity conditions. In the setting of our results we establish a situation in which a pair of mappings may possess common fixed points as well as coincidence points which may not be common fixed points. Our results generaliz...