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Volume 7, Issue 4
Strong Convergence Theorem Involving Two-Step Inertial Technique Without On-Line Rule for Split Feasibility Problem

Chibueze C. Okeke, Abubakar Adamu & Kalu O. Okorie

DOI: 10.12150/jnma.2025.1307

J. Nonl. Mod. Anal., 7 (2025), pp. 1307-1331.

Published online: 2025-07

[An open-access article; the PDF is free to any online user.]

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  • Abstract

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.

  • Keywords

Split feasibility problems, two-step inertial technique, CQ methods, strong convergence.

  • AMS Subject Headings

47H05, 47H10, 49J20, 47J25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-7-1307, author = {Okeke , Chibueze C.Adamu , Abubakar and Okorie , Kalu O.}, title = {Strong Convergence Theorem Involving Two-Step Inertial Technique Without On-Line Rule for Split Feasibility Problem}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2025}, volume = {7}, number = {4}, pages = {1307--1331}, abstract = {

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.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2025.1307}, url = {http://global-sci.org/intro/article_detail/jnma/24236.html} }
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 -

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.

Okeke , Chibueze C.Adamu , Abubakar and Okorie , Kalu O.. (2025). Strong Convergence Theorem Involving Two-Step Inertial Technique Without On-Line Rule for Split Feasibility Problem. Journal of Nonlinear Modeling and Analysis. 7 (4). 1307-1331. doi:10.12150/jnma.2025.1307
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