Some unified algorithms for finding minimum norm fixed point of nonexpansive semigroups in Hilbert spaces

In this paper, we introduce two general algorithms (one implicit and one explicit) for finding a common fixed point of a nonexpansive semigroup {T (s)}s≥0 in Hilbert spaces. We prove that both approaches converge strongly to a common fixed point of {T (s)}s≥0. Such common fixed point x∗ is the unique solution of some variational inequality, which is the optimality condition for some minimization problem. As special cases of the above two algorithms, we obtain two schemes which both converge strongly to the minimum norm common fixed point of {T (s)}s≥0.