Strong convergence theorems for solving equilibrium problems and fixed point problems of ξ-strict pseudo-contraction mappings by two hybrid projection methods

AbstractIn this paper, we introduce an iterative scheme by using the hybrid projection methods for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a ξ-strict pseudo-contraction mapping in Hilbert spaces. We obtain two strong convergence theorems under mild assumptions on parameters for the sequences generated by these processes. The results presented in the paper extend and improve some recent results of Marino and Xu [G. Marino, H.K. Xu, Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces, J. Math. Anal. Appl. 329 (2007) 336–346], Tada and Takahashi [A. Tada, W. Takahashi, Weak and strong convergence theorems for a nonexpansive mapping and an equilibrium problem, J. Optim. Theory Appl. 133 (2007) 359–370] and Ceng et al. [L.C. Ceng, S. Al-Homidan, Q.H. Ansari, J.C. Yao, An iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contraction mappings, J. Comput. Appl. Math. 223 (2009) 967–974] and many others