On a unified Yosida inclusion problem and its computational implications

Mohd. Falahat Khan; Syed Shakaib Irfan; Iqbal Ahmad; Ibrahim Karahan; Mohd. Falahat Khan; Syed Shakaib Irfan; Iqbal Ahmad; Ibrahim Karahan

doi:10.3934/math.2026470

AIMS Mathematics

2026, Volume 11, Issue 4: 11410-11436. doi: 10.3934/math.2026470

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Research article

On a unified Yosida inclusion problem and its computational implications

1.
Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
2.
Department of Mechanical Engineering, College of Engineering, Qassim University, Saudi Arabia
3.
Department of Mathematics, Faculty of Science, Erzurum Technical University, Erzurum, Turkey

Received: 19 January 2026 Revised: 04 April 2026 Accepted: 13 April 2026 Published: 24 April 2026
MSC : 47H05, 47H09, 47J22, 49J40

This paper introduced and considered the Yosida inclusion problem, which is a unified model arising from the monotone inclusion, fixed point, and Cayley inclusion problems. By using the Yosida operator as a regularized and generically differentiable approximation of a maximal monotone operator for solving the Yosida inclusion problem we devised efficient and stable iterative algorithms instead of direct resolvent computation. This approach offers both theoretical and computational advantages for solving complex mathematical operator inclusion problems in Hilbert spaces. We demonstrated that the sequence generated by the proposed inertial $ S $-iteration converges strongly. A theoretical example and an application were also presented to illustrate the effectiveness of the proposed algorithms.
- algorithms,
- image restoration,
- mathematical operator,
- optimization,
- monotone inclusion
Citation: Mohd. Falahat Khan, Syed Shakaib Irfan, Iqbal Ahmad, Ibrahim Karahan. On a unified Yosida inclusion problem and its computational implications[J]. AIMS Mathematics, 2026, 11(4): 11410-11436. doi: 10.3934/math.2026470

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Abstract

This paper introduced and considered the Yosida inclusion problem, which is a unified model arising from the monotone inclusion, fixed point, and Cayley inclusion problems. By using the Yosida operator as a regularized and generically differentiable approximation of a maximal monotone operator for solving the Yosida inclusion problem we devised efficient and stable iterative algorithms instead of direct resolvent computation. This approach offers both theoretical and computational advantages for solving complex mathematical operator inclusion problems in Hilbert spaces. We demonstrated that the sequence generated by the proposed inertial $ S $-iteration converges strongly. A theoretical example and an application were also presented to illustrate the effectiveness of the proposed algorithms.

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