A general hybrid relaxed CQ algorithm for solving the fixed-point problem and split-feasibility problem

Yuanheng Wang; Bin Huang; Bingnan Jiang; Tiantian Xu; Ke Wang; Yuanheng Wang; Bin Huang; Bingnan Jiang; Tiantian Xu; Ke Wang

doi:10.3934/math.20231239

AIMS Mathematics

2023, Volume 8, Issue 10: 24310-24330. doi: 10.3934/math.20231239

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A general hybrid relaxed CQ algorithm for solving the fixed-point problem and split-feasibility problem

School of Mathematic Science, Zhejiang Normal University, Jinhua 321004, China

Received: 02 May 2023 Revised: 02 July 2023 Accepted: 17 July 2023 Published: 14 August 2023
MSC : 47H04, 47H09, 47H10, 65K10

In this paper, we introduce a new hybrid relaxed iterative algorithm with two half-spaces to solve the fixed-point problem and split-feasibility problem involving demicontractive mappings. The strong convergence of the iterative sequence produced by our algorithm is proved under certain weak conditions. We give several numerical experiments to demonstrate the efficiency of the proposed iterative method in comparison with previous algorithms.
- inertial iterative method,
- demicontractive mapping,
- fixed point,
- hybrid CQ method,
- split-feasibility problem
Citation: Yuanheng Wang, Bin Huang, Bingnan Jiang, Tiantian Xu, Ke Wang. A general hybrid relaxed CQ algorithm for solving the fixed-point problem and split-feasibility problem[J]. AIMS Mathematics, 2023, 8(10): 24310-24330. doi: 10.3934/math.20231239

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Abstract

In this paper, we introduce a new hybrid relaxed iterative algorithm with two half-spaces to solve the fixed-point problem and split-feasibility problem involving demicontractive mappings. The strong convergence of the iterative sequence produced by our algorithm is proved under certain weak conditions. We give several numerical experiments to demonstrate the efficiency of the proposed iterative method in comparison with previous algorithms.

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