There exist many results in the literature regarding the iterative approximation of fixed points or common fixed points in the case of selfmappings, see, for example, the reviewer’s monograph [

*V. Berinde*, “Iterative approximation of fixed points” (Efemeride, Baia Mare) (2002;

Zbl 1036.47037)] for a recent survey. In the paper under review, the authors introduce and study a fixed point iterative procedure of Halpern type, constructed by means of the sunny nonexpansive retraction of

$K$, in order to approximate the common fixed points of a family of nonself nonexpansive mappings defined on a nonempty closed convex subset

$K$ of a Banach space satisfying some special geometric properties.