Some variant of Tseng splitting method with accelerated Visco-Cesaro means for monotone inclusion problems

Yasir Arfat; Supak Phiangsungnoen; Poom Kumam; Muhammad Aqeel Ahmad Khan; Jamshad Ahmad; Yasir Arfat; Supak Phiangsungnoen; Poom Kumam; Muhammad Aqeel Ahmad Khan; Jamshad Ahmad

doi:10.3934/math.20231254

AIMS Mathematics

2023, Volume 8, Issue 10: 24590-24608. doi: 10.3934/math.20231254

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Some variant of Tseng splitting method with accelerated Visco-Cesaro means for monotone inclusion problems

1.
KMUTT Fixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand
2.
Department of General Education (Mathematics), Faculty of Liberal Arts, Rajamangala University of Technology Rattanakosin, 264 Chakkrawat Rd, Chakkrawat, Samphanthawong, Bangkok, Thailand
3.
Institute of Research and Development, Rajamangala University of Technology Rattanakosin, 96 Phutthamonthon Sai 5 Road, Salaya, Phutthamonthon District, Nakhon Pathom 73170, Thailand
4.
Center of Excellence in Theoretical and Computational Science (TaCS-CoE), SCL 802 Fixed Point Laboratory, Science Laboratory Building, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand
5.
Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan
6.
Department of Mathematics, Faculty of Science, University of Gujrat, Gujrat, 50700, Pakistan

Received: 25 March 2023 Revised: 18 July 2023 Accepted: 08 August 2023 Published: 21 August 2023
MSC : 47H05, 47H06, 47H09, 47H10, 65K15, 65Y05, 68W10

In this paper, we examine the convergence analysis of a variant of Tseng's splitting method for monotone inclusion problem and fixed point problem associated with an infinite family of $ \eta $-demimetric mappings in Hilbert spaces. The qualitative results of the proposed variant shows strong convergence characteristics under a suitable set of control conditions. We also provide a numerical example to demonstrate the applicability of the variant with some applications.
- monotone inclusion problem,
- forward-backward-forward method,
- viscosity method,
- Ces$ \acute{a} $ro means method,
- Nesterov's accelerated method
Citation: Yasir Arfat, Supak Phiangsungnoen, Poom Kumam, Muhammad Aqeel Ahmad Khan, Jamshad Ahmad. Some variant of Tseng splitting method with accelerated Visco-Cesaro means for monotone inclusion problems[J]. AIMS Mathematics, 2023, 8(10): 24590-24608. doi: 10.3934/math.20231254

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Abstract

In this paper, we examine the convergence analysis of a variant of Tseng's splitting method for monotone inclusion problem and fixed point problem associated with an infinite family of $ \eta $-demimetric mappings in Hilbert spaces. The qualitative results of the proposed variant shows strong convergence characteristics under a suitable set of control conditions. We also provide a numerical example to demonstrate the applicability of the variant with some applications.

References

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