Strong convergence theorem for nonexpansive mappings on star-shaped sets in Hilbert spaces

In this paper, using the concept of attractive points of a nonlinear mapping, we obtain a strong convergence theorem of Halpern's type [7] for nonexpansive mappings in a star-shaped subset of a Hilbert space. Using this result, we obtain a new fixed point theorem and a strong convergence theorem which generalizes Wittmann's theorem [26].