An estimation of deviation of fixed points from a~nonconvex set

N. M. Gulevich

Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part IV, Tome 122 (1982), pp. 13-16

Résumé

In. this notes the estimation $\delta(F_i\times f, A)\leqslant2^{-\frac12}d(A)$, is given, where $A$ is an nonvoid closed bounded nonconvex set in a Hilbert space $H$, $f\colon\overline{\operatorname{co}}A\to H$ is a nonexpansive mapping and $f(\partial A)\subset A$, $\delta(F_i\times f, A)$ is the deviation of the fixed point set of a mapping $f$ from the set $A$, $d(A)$ is the diameter of the set $A$, $\partial A$ is the boundary of the set $A$ in $H$.