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

Hasanen A. Hammad; Habib ur Rehman; Manuel De la Sen; Hasanen A. Hammad; Habib ur Rehman; Manuel De la Sen

doi:10.3934/math.2025720

AIMS Mathematics

2025, Volume 10, Issue 7: 16068-16104. doi: 10.3934/math.2025720

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

1.
Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
2.
School of Mathematics, Zhejiang Normal University, Jinhua 321004, China
3.
Institute of Research and Development of Processes, Department of Electricity and Electronics, Faculty of Science and Technology, University of the Basque Country, 48940-Leioa (Bizkaia), Spain

Received: 14 May 2025 Revised: 17 June 2025 Accepted: 04 July 2025 Published: 17 July 2025
MSC : 47H10, 47J25, 65K15

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.
- convergence result,
- numerical method,
- Hilbert space,
- demicontractive mapping,
- split fixed point problem
Citation: Hasanen A. Hammad, Habib ur Rehman, Manuel De la Sen. Convergence behavior of practical iterative schemes for split fixed point problems under fixed and variable stepsize strategies[J]. AIMS Mathematics, 2025, 10(7): 16068-16104. doi: 10.3934/math.2025720

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Abstract

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.

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