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Research Article | Open Access

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

Yasir Arfat1, Supak Phiangsungnoen2,3( ), Poom Kumam1,4, Muhammad Aqeel Ahmad Khan5, Jamshad Ahmad6
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
Department of General Education (Mathematics), Faculty of Liberal Arts, Rajamangala University of Technology Rattanakosin, 264 Chakkrawat Rd, Chakkrawat, Samphanthawong, Bangkok, Thailand
Institute of Research and Development, Rajamangala University of Technology Rattanakosin, 96 Phutthamonthon Sai 5 Road, Salaya, Phutthamonthon District, Nakhon Pathom 73170, Thailand
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
Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan
Department of Mathematics, Faculty of Science, University of Gujrat, Gujrat, 50700, Pakistan
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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 η-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.

Keywords

monotone inclusion problemforward-backward-forward methodviscosity methodCesáro means methodNesterov's accelerated method
CLC number: 47H05, 47H06, 47H09, 47H10, 65K15, 65Y05, 68W10

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AIMS Mathematics
Volume 8 Issue 10,
October 2023
Pages 24590-24608
DOI: 10.3934/math.20231254

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Arfat Y, Phiangsungnoen S, Kumam P, et al. Some variant of Tseng splitting method with accelerated Visco-Cesaro means for monotone inclusion problems. AIMS Mathematics, 2023, 8(10): 24590-24608. https://doi.org/10.3934/math.20231254

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Received: 25 March 2023
Revised: 18 July 2023
Accepted: 08 August 2023
Published: 15 October 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)