## On strong convergence to common fixed points of nonexpansive semigroups in Hilbert spaces.(English)Zbl 1031.47038

Let $$C$$ be a closed convex subset of a Hilbert space $$H$$. Also, let $$\{T(t);t\geq 0\}$$ be a strongly continuous semigroup of nonexpansive maps on $$C$$ such that $$F(T)$$ (the set of its common fixed points) is nonvoid. Fix $$u\in C$$ and define the sequence $$(u_n)$$ in $$C$$ as $$(u_n=(1-\alpha_n)T(t_n)u_n+\alpha_n u,\;n\in \mathbb{N})$$, where $$(\alpha_n)$$ in $$]0,1[$$ and $$(t_n)$$ in $$]0,\infty[$$ satisfy $$\lim_n (t_n)=\lim_n(\alpha_n/t_n)=0$$. Then, $$(u_n)$$ converges strongly to the element of $$F(T)$$ nearest to $$u$$.

### MSC:

 47H20 Semigroups of nonlinear operators 47H10 Fixed-point theorems
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### References:

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