  In this paper, we show that, under appropriate conditions, there exists a
quasinonexpansive extension of a mapping with an attractive point in the sense
of Takahashi and Takeuchi (2011) such that the fixed point set of the extension
equals the attractive point set of the given mapping. Then using the
quasinonexpansive extension, we establish some convergence theorems for
approximating attractive points of a generalized hybrid mapping in the sense of
Kocourek, Takahashi, and Yao (2010).
