Convergence analysis of Mann-type hybrid inertial Yosida approximation iterative schemes for split variational inclusions

Doaa Filali; Mohammad Dilshad; Mohammad Akram; Md. Nasiruzzaman; Esmail Alshaban; Doaa Filali; Mohammad Dilshad; Mohammad Akram; Md. Nasiruzzaman; Esmail Alshaban

doi:10.3934/math.2026399

AIMS Mathematics

2026, Volume 11, Issue 4: 9633-9654. doi: 10.3934/math.2026399

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Research article

Convergence analysis of Mann-type hybrid inertial Yosida approximation iterative schemes for split variational inclusions

1.
Department of Mathematical Science, College of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk-71491, Saudi Arabia
3.
Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah-107, Saudi Arabia

Received: 17 January 2026 Revised: 16 March 2026 Accepted: 02 April 2026 Published: 10 April 2026
MSC : 47H05, 47H06, 49J40

This manuscript introduces two Mann-type hybrid inertial Yosida approximation iterative schemes for exploring a split variational inclusion problem and a fixed point of a nonexpansive mapping. Unlike existing methods, our schemes initiate the process by computing a Mann-type iteration that incorporates both an inertial extrapolation and a fixed-point iteration. The Yosida approximation operators associated with the corresponding monotone mappings are employed. We establish strong convergence theorems for the proposed schemes under suitable assumptions without estimating the norm of a bounded linear operator. Numerical examples are presented to validate the theoretical results, and a comparison of the proposed iterative schemes with existing methods is provided. Finally, an application of our schemes for solving the split common fixed point problem (SCFPP) is also discussed.
- split variational inclusion,
- fixed point,
- Inertial,
- algorithm,
- Yosida approximation,
- strong convergence
Citation: Doaa Filali, Mohammad Dilshad, Mohammad Akram, Md. Nasiruzzaman, Esmail Alshaban. Convergence analysis of Mann-type hybrid inertial Yosida approximation iterative schemes for split variational inclusions[J]. AIMS Mathematics, 2026, 11(4): 9633-9654. doi: 10.3934/math.2026399

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Abstract

This manuscript introduces two Mann-type hybrid inertial Yosida approximation iterative schemes for exploring a split variational inclusion problem and a fixed point of a nonexpansive mapping. Unlike existing methods, our schemes initiate the process by computing a Mann-type iteration that incorporates both an inertial extrapolation and a fixed-point iteration. The Yosida approximation operators associated with the corresponding monotone mappings are employed. We establish strong convergence theorems for the proposed schemes under suitable assumptions without estimating the norm of a bounded linear operator. Numerical examples are presented to validate the theoretical results, and a comparison of the proposed iterative schemes with existing methods is provided. Finally, an application of our schemes for solving the split common fixed point problem (SCFPP) is also discussed.

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