Adaptive inertial Yosida approximation iterative algorithms for split variational inclusion and fixed point problems

Mohammad Dilshad; Mohammad Akram; Md. Nasiruzzaman; Doaa Filali; Ahmed A. Khidir; Mohammad Dilshad; Mohammad Akram; Md. Nasiruzzaman; Doaa Filali; Ahmed A. Khidir

doi:10.3934/math.2023651

AIMS Mathematics

2023, Volume 8, Issue 6: 12922-12942. doi: 10.3934/math.2023651

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Research article

Adaptive inertial Yosida approximation iterative algorithms for split variational inclusion and fixed point problems

1.
Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah-107, Saudi Arabia
3.
Department of Mathematical Science, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh, Saudi Arabia
4.
Faculty of Technology of Mathematical Sciences and Statistics, Alneelain University, Khartoum, Sudan

Received: 16 January 2023 Revised: 08 March 2023 Accepted: 21 March 2023 Published: 31 March 2023
MSC : 47H05, 47H06, 49J40

In this paper, we present self-adaptive inertial iterative algorithms involving Yosida approximation to investigate a split variational inclusion problem (SVIP) and common solutions of a fixed point problem (FPP) and SVIP in Hilbert spaces. We analyze the weak convergence of the proposed iterative algorithm to explore the approximate solution of the SVIP and strong convergence to estimate the common solution of the SVIP and FPP under some mild suppositions. A numerical example is demonstrated to validate the theoretical findings, and comparison of our iterative methods with some known schemes is outlined.
- split variational inclusion,
- fixed point problem,
- Yosida approximation,
- algorithms,
- weak convergence,
- strong convergence
Citation: Mohammad Dilshad, Mohammad Akram, Md. Nasiruzzaman, Doaa Filali, Ahmed A. Khidir. Adaptive inertial Yosida approximation iterative algorithms for split variational inclusion and fixed point problems[J]. AIMS Mathematics, 2023, 8(6): 12922-12942. doi: 10.3934/math.2023651

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Abstract

In this paper, we present self-adaptive inertial iterative algorithms involving Yosida approximation to investigate a split variational inclusion problem (SVIP) and common solutions of a fixed point problem (FPP) and SVIP in Hilbert spaces. We analyze the weak convergence of the proposed iterative algorithm to explore the approximate solution of the SVIP and strong convergence to estimate the common solution of the SVIP and FPP under some mild suppositions. A numerical example is demonstrated to validate the theoretical findings, and comparison of our iterative methods with some known schemes is outlined.

References

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