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The purpose of this paper is to introduce and study a modified Halpern's iterative scheme for solving the split feasibility problem SFP in the setting of infinite-dimensional Hilbert spaces. Under suitable conditions a strong convergence theorem is established. The main result presented in this paper improves and extends some recent results done by Xu Iterative methods for the split feasibility problem in infinite-dimensional Hilbert space, Inverse Problem 26 2010 105018 and some others.

In this paper, we introduce and study an iterative viscosity approximation method by modified Cesàro mean approximation for finding a common solution of split generalized equilibrium, variational inequality and fixed point problems. Under suitable conditions, we prove a strong convergence theorem for the sequences generated by the proposed iterative scheme. The results presented in this paper generalize, extend and improve the corresponding results of Shimizu