Projection methods for quasi-nonexpansive multivalued mappings in Hilbert spaces

Anantachai Padcharoen; Kritsana Sokhuma; Jamilu Abubakar; Anantachai Padcharoen; Kritsana Sokhuma; Jamilu Abubakar

doi:10.3934/math.2023364

AIMS Mathematics

2023, Volume 8, Issue 3: 7242-7257. doi: 10.3934/math.2023364

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Research article

Projection methods for quasi-nonexpansive multivalued mappings in Hilbert spaces

1.
Department of Mathematics, Faculty of Science and Technology, Rambhai Barni Rajabhat University, Chanthaburi 22000, Thailand
2.
Department of Mathematics, Faculty of Science and Technology, Phranakhon Rajabhat University, Bangkok 10220, Thailand
3.
Department of Mathematics, Usmanu Danfodiyo University, Sokoto 840004, Nigeria

Received: 29 August 2022 Revised: 02 December 2022 Accepted: 28 December 2022 Published: 12 January 2023
MSC : 47H09, 47H10

This paper proposes a modified D-iteration to approximate the solutions of three quasi-nonexpansive multivalued mappings in a real Hilbert space. Due to the incorporation of an inertial step in the iteration, the sequence generated by the modified method converges faster to the common fixed point of the mappings. Furthermore, the generated sequence strongly converges to the required solution using a shrinking technique. Numerical results obtained indicate that the proposed iteration is computationally efficient and outperforms the standard forward-backward with inertial step.
- quasi-nonexpansive multivalued mappings,
- weak and strong convergence,
- inertial technical term,
- D-iteration,
- projection methods
Citation: Anantachai Padcharoen, Kritsana Sokhuma, Jamilu Abubakar. Projection methods for quasi-nonexpansive multivalued mappings in Hilbert spaces[J]. AIMS Mathematics, 2023, 8(3): 7242-7257. doi: 10.3934/math.2023364

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Abstract

This paper proposes a modified D-iteration to approximate the solutions of three quasi-nonexpansive multivalued mappings in a real Hilbert space. Due to the incorporation of an inertial step in the iteration, the sequence generated by the modified method converges faster to the common fixed point of the mappings. Furthermore, the generated sequence strongly converges to the required solution using a shrinking technique. Numerical results obtained indicate that the proposed iteration is computationally efficient and outperforms the standard forward-backward with inertial step.

References

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