Approximating solutions to a class of split feasibility problems in Banach spaces

Abstract We study the split common solution problem with multiple output sets for monotone operator equations in Banach spaces. We first show that any weak limit point of the sequence generated by our algorithm is a solution to the problem and then we establish the weak convergence of the sequence to a solution. Subsequently, using Halpern’s regularization method, we obtain the strong convergence of the sequence generated by a modified algorithm to a solution of the problem.