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Simple inertial methods for solving split variational inclusions in Banach Spaces
  • Aviv Gibali,
  • Yeol Je Cho
Chongqing Technology and Business University
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Aviv Gibali
ORT Braude College
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Yeol Je Cho
Gyeongsang National University
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In this paper, we introduce two simple inertial algorithms for solving the split variational inclusion problem in Banach spaces. Under mild and standard assumptions we establish the weak and strong convergence of the proposed methods, respectively. As theoretical realization we study existence of solutions of the split common fixed point problem in Banach spaces.

Several numerical examples in finite and infinite dimensional spaces compare and illustrate the performances of our schemes. Our work generalize and extend some recent relate results in the literature and also propose a simple and applicable method for solving split variational inclusions.

2000 Mathematics Subject Classification: 65K10; 65K05; 47H10; 47L25.

Keywords: Split variational inclusion problem; inertial technique; Banach spaces.

Peer review status:ACCEPTED

14 Jun 2020Submitted to Mathematical Methods in the Applied Sciences
19 Jun 2020Submission Checks Completed
19 Jun 2020Assigned to Editor
18 Jul 2020Reviewer(s) Assigned
28 Oct 2020Review(s) Completed, Editorial Evaluation Pending
15 Nov 2020Editorial Decision: Revise Major
17 Jan 20211st Revision Received
17 Jan 2021Submission Checks Completed
17 Jan 2021Assigned to Editor
22 Jan 2021Reviewer(s) Assigned
03 Feb 2021Review(s) Completed, Editorial Evaluation Pending
12 May 2021Editorial Decision: Accept