Convergence behavior of practical iterative schemes for split fixed point problems under fixed and variable stepsize strategies

This work presents a practical iterative algorithm, extending the inertial Mann iteration, for solving split fixed-point problems with demicontractive mappings in real Hilbert spaces. We rigorously establish both its weak and strong convergence under clearly defined parametric conditions. Our methodology utilizes versatile two-step selection techniques with both fixed and variable step sizes. Compelling numerical experiments confirm the algorithm's accuracy and computational efficiency in approximating solutions to these challenging problems.