Browder's convergence for uniformly asymptotically regular nonexpansive semigroups in Hilbert spaces
Let \(C\) be a closed convex subset of a Hilbert space and \((T(t):t\geq 0)\) be a uniformly asymptotically regular nonexpansive semigroup on \(C\) with \(F:=\cap\{F(T(t)):t\geq 0\}\neq \emptyset\). Let \((a_n)\subset (0,1)\) and \((t_n)\subset (0,\infty)\) be sequences with \(\lim_n(a_n)=\lim_n(a_n/t_n)=0\). Then, for each \(u\in C\), the implicit sequence \[ x_n=a_nu+(1-a_n)T(t_n)x_n, \quad n\geq 0, \] converges strongly to an element of \(F\), nearest to \(u\).
one-parameter strongly continuous semigroup of nonexpansive mappings
scientific article; zbMATH DE number 5692331
scientific article