The authors provide a result strictly related to Theorem 1 in [A. Tada and W. Takahashi, Proc. NACA (Okinawa, 2005), 609–617 (2007; Zbl 1122.47055), reviewed above]. Indeed, they consider the equilibrium problem: find such that
where is a nonempty, closed and convex subset of a real Hilbert space , and . The set of solutions is denoted by .
Under the same assumptions of Theorem 1, and given in addition a contraction , they find a way to generate two sequences of points, namely and , approximating in the viscosity sense the equilibria that are also the fixed points of a nonexpansive map , i.e., both of them converge strongly to a point , where is the projection of onto . As corollaries, they get results previously obtained by R. Wittman [Arch. Math. 58, No. 5, 486–491 (1992; Zbl 0797.47036)] and P. L. Combettes and S. A. Hirstoaga [J. Nonlinear Convex Anal. 6, No. 1, 117–136 (2005; Zbl 1109.90079)].