Abstract
In this paper, we consider the Halpern iteration for $$\alpha $$ -nonexpansive mapping semigroups; such semigroups contain classical nonexpansive mapping semigroups as special cases. The strong convergence theorems of Halpern iteration sequence are shown for finding a common fixed point of an $$\alpha $$ -nonexpansive semigroup, which exactly is a metric projection point of the anchor point u to the common fixed point set of such semigroups. Furthermore, the strong convergence of the Halpern iteration for an $$\alpha $$ -nonexpansive mapping sequence is given also.
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