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Multi-inertial parallel hybrid projection algorithm for generalized split null point problems

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Abstract

In this paper we suggest a theoretical framework to study the generalized split null point problem (GSNPP) via a multi-step inertial based parallel hybrid projection algorithm in Hilbert spaces. The architecture and the suitable set of control conditions ensure the strong convergence of the algorithm. The possible applications of the algorithm are illustrated via various theoretical and numerical results. The key advantages of the algorithm are highlighted in comparison to the classical and non-inertial algorithm as well as (one-step and two-step) inertial variants of the algorithm for the GSNPP.

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Acknowledgements

The authors wish to thank the anonymous referees for their comments and suggestions. The authors (Y. Arfat and P. Kumam) acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. Moreover, this project is funded by National Council of Thailand (NRCT) under Research Grants for Talented Mid-Career Researchers (Contract no. N41A640089). The author Y. Arfat was supported by the Petchra Pra Jom Klao Ph.D Research Scholarship from King Mongkut’s University of Technology Thonburi, Thailand (Grant No.16/2562).

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Authors and Affiliations

  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

    Yasir Arfat & Poom Kumam

  2. 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

    Poom Kumam

  3. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan

    Poom Kumam

  4. Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore, 54000, Pakistan

    Muhammad Aqeel Ahmad Khan

  5. Department of Mathematics, Clarkson University, Potsdam, NY, USA

    Olaniyi S. Iyiola

Authors
  1. Yasir Arfat
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  2. Poom Kumam
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  3. Muhammad Aqeel Ahmad Khan
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  4. Olaniyi S. Iyiola
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All authors contributed equally and significantly in writing this article. All authors read and approved the final manuscript.

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Correspondence to Poom Kumam.

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Arfat, Y., Kumam, P., Khan, M.A.A. et al. Multi-inertial parallel hybrid projection algorithm for generalized split null point problems. J. Appl. Math. Comput. 68, 3179–3198 (2022). https://doi.org/10.1007/s12190-021-01660-4

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