An inertially constructed projection based hybrid algorithm for fixed point and split null point problems

Yasir Arfat; Poom Kumam; Supak Phiangsungnoen; Muhammad Aqeel Ahmad Khan; Hafiz Fukhar-ud-din; Yasir Arfat; Poom Kumam; Supak Phiangsungnoen; Muhammad Aqeel Ahmad Khan; Hafiz Fukhar-ud-din

doi:10.3934/math.2023333

AIMS Mathematics

2023, Volume 8, Issue 3: 6590-6608. doi: 10.3934/math.2023333

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An inertially constructed projection based hybrid algorithm for fixed point and split null point problems

1.
Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangkok 10140, Thailand
2.
Center of Excellence in Theoretical and Computational Science (TaCS-CoE), King Mongkut's University of Technology Thonburi (KMUTT), Bangkok 10140, Thailand
3.
China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
4.
Department of General Education (Mathematics), Faculty of Liberal Arts, Rajamangala University of Technology Rattanakosin, Samphanthawong, Bangkok, Thailand
5.
Institute of Research and Development, Rajamangala University of Technology Rattanakosin, Nakhon Pathom 73170, Thailand
6.
Department of Mathematics, COMSATS University Islamabad, Lahore 54000, Pakistan
7.
Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan

Received: 29 July 2022 Revised: 29 November 2022 Accepted: 12 December 2022 Published: 05 January 2023
MSC : 47H05, 47H10, 47J25, 49M30, 54H25

In this paper, we posit a framework for the investigation of the fixed point problems (FPP) involving an infinite family of $ \Bbbk $-demicontractive operators and the split common null point problems (SCNPP) in Hilbert spaces. We employ an accelerated variant of the hybrid shrinking projection algorithm for the construction of a common solution associated with the FPP and SCNPP. Theoretical results comprise strong convergence characteristics under suitable sets of constraints as well as numerical results are established for the underlying algorithm. Applications to signal processing as well as various abstract problems are also incorporated.
- hybrid algorithm,
- inertial extrapolation,
- strong convergence,
- fixed point problem,
- demicontractive operator,
- null point problem
Citation: Yasir Arfat, Poom Kumam, Supak Phiangsungnoen, Muhammad Aqeel Ahmad Khan, Hafiz Fukhar-ud-din. An inertially constructed projection based hybrid algorithm for fixed point and split null point problems[J]. AIMS Mathematics, 2023, 8(3): 6590-6608. doi: 10.3934/math.2023333

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Abstract

In this paper, we posit a framework for the investigation of the fixed point problems (FPP) involving an infinite family of $ \Bbbk $-demicontractive operators and the split common null point problems (SCNPP) in Hilbert spaces. We employ an accelerated variant of the hybrid shrinking projection algorithm for the construction of a common solution associated with the FPP and SCNPP. Theoretical results comprise strong convergence characteristics under suitable sets of constraints as well as numerical results are established for the underlying algorithm. Applications to signal processing as well as various abstract problems are also incorporated.

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