A self-adaptive inertial approximation method for split equality fixed point problems of $ k $-demimetric mappings in Banach spaces

Chanjuan Pan; Yan Zhang; Panpan Zhu; Kunyang Wang; Chanjuan Pan; Yan Zhang; Panpan Zhu; Kunyang Wang

doi:10.3934/math.20261321

AIMS Mathematics

2026, Volume 11, Issue 10: 33811-33834. doi: 10.3934/math.20261321

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Research article

A self-adaptive inertial approximation method for split equality fixed point problems of $ k $-demimetric mappings in Banach spaces

1.
School of Computer Science and Technology, Zhejiang University of Water Resources and Electric Power, Hangzhou, 310018, China
2.
Key Laboratory of Rare Earth Optoelectronic Materials and Devices of Zhejiang Province, Institute of Optoelectronic Materials and Devices, China Jiliang University, Hangzhou, 310018, China

Received: 22 July 2026 Revised: 09 September 2026 Accepted: 21 September 2026 Published: 19 October 2026
MSC : 47H06, 47H09, 47J05, 47J25

In this paper, we investigate the split equality fixed point problems for $ k $-demimetric mappings in Banach spaces. A self-adaptive inertial approximation method is developed by incorporating an adaptive inertial prediction mechanism, a Landweber-type correction step for the split equality constraint, and a $ k $-demimetric fixed point approximation procedure. Under suitable assumptions, the proposed method generates a sequence that converges strongly to the Bregman projection of the anchor point onto the solution set. Furthermore, the obtained results are applied to split equality variational inclusion problems and split equality equilibrium problems. Numerical experiments are conducted to verify the effectiveness of the proposed method.
- split equality fixed point problem,
- self-adaptive inertial algorithm,
- $ k $-demimetric mappings,
- strong convergence,
- Banach space
Citation: Chanjuan Pan, Yan Zhang, Panpan Zhu, Kunyang Wang. A self-adaptive inertial approximation method for split equality fixed point problems of $ k $-demimetric mappings in Banach spaces[J]. AIMS Mathematics, 2026, 11(10): 33811-33834. doi: 10.3934/math.20261321

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Abstract

In this paper, we investigate the split equality fixed point problems for $ k $-demimetric mappings in Banach spaces. A self-adaptive inertial approximation method is developed by incorporating an adaptive inertial prediction mechanism, a Landweber-type correction step for the split equality constraint, and a $ k $-demimetric fixed point approximation procedure. Under suitable assumptions, the proposed method generates a sequence that converges strongly to the Bregman projection of the anchor point onto the solution set. Furthermore, the obtained results are applied to split equality variational inclusion problems and split equality equilibrium problems. Numerical experiments are conducted to verify the effectiveness of the proposed method.

References

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