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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. LOMI, 1982 Volume 122, Pages 13–16 (Mi znsl4035)

An estimation of deviation of fixed points from a nonconvex set

N. M. Gulevich


Abstract: 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 $H$.

UDC: 515.126.4, 517.988.52



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© Steklov Math. Inst. of RAS, 2024