A SHRINKING PROJECTION APPROACH FOR SPLIT EQUILIBRIUM PROBLEMS AND FIXED POINT PROBLEMS IN HILBERT SPACES

In this work, we employ the iterative shrinking projection algorithm to find an approximate common solution to an equilibrium problem and a fixed point problem in the setting of Hilbert spaces. In particular, we establish strong convergence of the proposed iterative algorithm towards a common element in the set of solutions of a finite family of split equilibrium problems and the set of common fixed points of a finite family of total asymptotically nonexpansive mappings in such setting. Our results can be viewed as a generalization and improvement of various existing results in the current literature.