Strong convergence theorems for an implicit iterative algorithm for the split common fixed point problem (Q503502)

Summary: The aim of this paper is to construct a novel implicit iterative algorithm for the split common fixed point problem for the demicontractive operators \(U, T\), and \(x_n = \alpha_n f \left(x_n\right) + \left(1 - \alpha_n\right) U_\lambda \left(x_n - \rho_n A^* \left(I - T\right) A x_n\right)\), \(n \geq 0\), where \(U_\lambda = (1 - \lambda) I + \lambda U\), and we obtain the sequence which strongly converges to a solution \(\hat{x}\) of this problem, and the solution \(\hat{x}\) satisfies the variational inequality. \(\langle \hat{x} - f(\hat{x}), \hat{x} - z \rangle \leq 0\), \(\forall z \in S\), where \(S\) denotes the set of all solutions of the split common fixed point problem.