TY - JOUR
T1 - Strong Convergence Theorem Involving Two-Step Inertial Technique Without On-Line Rule for Split Feasibility Problem
AU - Okeke , Chibueze C.
AU - Adamu , Abubakar
AU - Okorie , Kalu O.
JO - Journal of Nonlinear Modeling and Analysis
VL - 4
SP - 1307
EP - 1331
PY - 2025
DA - 2025/07
SN - 7
DO - http://doi.org/10.12150/jnma.2025.1307
UR - https://global-sci.org/intro/article_detail/jnma/24236.html
KW - Split feasibility problems, two-step inertial technique, CQ methods, strong convergence.
AB - <p style="text-align: justify;">This work presents an approach for solving the split feasibility
problem in an efficient manner. For solving the split feasibility problem, we
present 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 decreased
computational complexity. The strong convergence results are obtained without on-line rule of the inertial parameters and the iterates. This makes our
proof arguments different from what is obtainable in the literature where online rule is imposed on algorithms involving inertial extrapolation step. As far
as we know, no strong convergence result has been obtained before now for
algorithms with two step inertial for solving split feasibility problems in the
literature. To demonstrate the viability of our suggested strategy, numerical
results are provided at the end.</p>