Strong Convergence Theorem Involving Two-Step Inertial Technique Without On-Line Rule for Split Feasibility Problem (Journal of Nonlinear Modeling and Analysis, 2025)
This work presents an approach for solving the split feasibilityproblem in an efficient manner. For solving the split feasibility problem, wepresent a method with a two-step inertial extrapolation and self-adaptive stepsize. The adjustable stepsize and two-step inertial extrapolation both contribute to the proposed method’s improved rate of convergence and decreasedcomputational complexity. The strong convergence results are obtained without on-line rule of the inertial parameters and the iterates. This makes ourproof arguments different from what is obtainable in the literature where online rule is imposed on algorithms involving inertial extrapolation step. As faras we know, no strong convergence result has been obtained before now foralgorithms with two step inertial for solving split feasibility problems in theliterature. To demonstrate the viability of our suggested strategy, numericalresults are provided at the end.