Strongly Convergent Iterative Methods for Generalized Split Feasibility Problems in Hilbert Spaces

Motivated by the idea of the split feasibility problem and results for solving the problem, we consider generalized split feasibility problems and then establish two Halpern type strong convergence theorems which are related to the problems. Furthermore, we prove strong convergence of an iterative scheme generated by the shrinking projection method. As applications, we get new and well-known strong convergence theorems which are connected with fixed point problem, split feasibility problem and equilibrium problem.