| In this paper, we introduce an iterative scheme by Cesàro means for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of an equilibrium problem in a Hilbert space. Then, we show that the sequence converges weakly to a common element of these two sets. Using this result, we obtain a generalization of the well-known nonlinear ergodic theorem by Baillon. Further, we consider the problem of finding a common point of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem for a monotone mapping in a Hilbert space. |
|
