A general alternative regularization method with line search technique for solving split equilibrium and fixed point problems in Hilbert spaces

In this paper, we introduce a new general alternative regularization algorithm for solving split equilibrium and fixed point problems in real Hilbert spaces. The proposed method does not require a prior estimate of the norm of the bounded linear operator nor a fixed stepsize for its convergence. Instead, we employ a line search technique and prove a strong convergence result for the sequence generated by the algorithm. A numerical experiment is given to show that the proposed method converges faster in terms of number of iteration and CPU time of computation than some existing methods in the literature.