Generalized extragradient iterative methods for solving split feasibility and fixed point problems in Hilbert spaces

In the paper, we analyze the extragradient method with regularization for finding a common element of the solution set of the split feasibility and fixed point problems of pseudo-contractive mappings. Moreover we propose the extragradient with regularization iterative method due to a generalized Ishikawa-type and Mann-type iterative methods. The weak convergence theorems of the sequences generated by the proposed iterative methods are obtained under the certain assumptions on pseudo-contractive mappings in real Hilbert spaces. Finally, we give the numerical example to demonstrate the effectiveness of our theoretical results and compare its behavior with the iterative methods of Ceng et al. (Fixed Point Theory Appl 192, 2015).