A new self-adaptive inertial algorithm with $ W $-mapping for solving split feasibility problem in Banach spaces

Meiying Wang; Luoyi Shi; Meiying Wang; Luoyi Shi

doi:10.3934/math.20221032

AIMS Mathematics

2022, Volume 7, Issue 10: 18767-18783. doi: 10.3934/math.20221032

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Research article

A new self-adaptive inertial algorithm with $ W $-mapping for solving split feasibility problem in Banach spaces

Meiying Wang ¹,
Luoyi Shi ^{1,2
,
,}

1.
School of Mathematical Sciences, Tiangong University, Tianjin 300387, China
2.
School of Software, Tiangong University, Tianjin 300387, China

Received: 22 June 2022 Revised: 07 August 2022 Accepted: 16 August 2022 Published: 23 August 2022
MSC : 47H09, 47J25

In this paper, the split feasibility problem is studied in real Banach spaces. Through the $ W $-mapping, a new iterative algorithm with the inertial technique for solving the split feasibility problem is proposed, which the step size is self-adaptive and no prior estimation of operator norm is required. We prove that the proposed algorithm converges weakly to a solution of the split feasibility problem under some mild conditions. Finally, the effectiveness of the proposed algorithm is indicated by numerical experiments. Our results are innovative and can enrich recently announced related results in the literature.
- split feasibility problem,
- inertial technique,
- $ W $-mapping,
- weak convergence,
- Banach spaces
Citation: Meiying Wang, Luoyi Shi. A new self-adaptive inertial algorithm with $ W $-mapping for solving split feasibility problem in Banach spaces[J]. AIMS Mathematics, 2022, 7(10): 18767-18783. doi: 10.3934/math.20221032

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Abstract

In this paper, the split feasibility problem is studied in real Banach spaces. Through the $ W $-mapping, a new iterative algorithm with the inertial technique for solving the split feasibility problem is proposed, which the step size is self-adaptive and no prior estimation of operator norm is required. We prove that the proposed algorithm converges weakly to a solution of the split feasibility problem under some mild conditions. Finally, the effectiveness of the proposed algorithm is indicated by numerical experiments. Our results are innovative and can enrich recently announced related results in the literature.

References

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