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AIMS Mathematics

2023, Volume 8, Issue 5: 11037-11056. doi: 10.3934/math.2023559
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A generalized Halpern-type forward-backward splitting algorithm for solving variational inclusion problems

  • 1.
    Mathematics, Department of Learning Management, Faculty of Education, Burapha University, Chonburi Campus, 169 Long Haad Bangsaen Road, Saen Suk, Mueang, Chonburi 20131, Thailand
  • 2.
    Center of Excellence in Theoretical and Computational Science, SCL 802 Fixed Point Laboratory, Science Laboratory Building, King Mongkut's University of Technology Thonburi, 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand
  • 3.
    Mathematics Institute, African University of Science and Technology, Abuja 900107, Nigeria
  • 4.
    Operational Research Center in Healthcare, Near East University, Nicosia, TRNC, Turkey
  • 5.
    KMUTTFixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi, 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand
  • 6.
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
  • Received: 15 August 2022 Revised: 18 January 2023 Accepted: 02 February 2023 Published: 08 March 2023

  • MSC : 46N10, 90C25

  • In this paper, we investigate the problem of finding a zero of sum of two accretive operators in the setting of uniformly convex and $ q $-uniformly smooth real Banach spaces ($ q > 1 $). We incorporate the inertial and relaxation parameters in a Halpern-type forward-backward splitting algorithm to accelerate the convergence of its sequence to a zero of sum of two accretive operators. Furthermore, we prove strong convergence of the sequence generated by our proposed iterative algorithm. Finally, we provide a numerical example in the setting of the classical Banach space $ l_4(\mathbb{R}) $ to study the effect of the relaxation and inertial parameters in our proposed algorithm.

    Citation: Premyuda Dechboon, Abubakar Adamu, Poom Kumam. A generalized Halpern-type forward-backward splitting algorithm for solving variational inclusion problems[J]. AIMS Mathematics, 2023, 8(5): 11037-11056. doi: 10.3934/math.2023559

    Related Papers:

  • In this paper, we investigate the problem of finding a zero of sum of two accretive operators in the setting of uniformly convex and $ q $-uniformly smooth real Banach spaces ($ q > 1 $). We incorporate the inertial and relaxation parameters in a Halpern-type forward-backward splitting algorithm to accelerate the convergence of its sequence to a zero of sum of two accretive operators. Furthermore, we prove strong convergence of the sequence generated by our proposed iterative algorithm. Finally, we provide a numerical example in the setting of the classical Banach space $ l_4(\mathbb{R}) $ to study the effect of the relaxation and inertial parameters in our proposed algorithm.


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