A self-adaptive viscosity-type inertial algorithm for common solutions of generalized split variational inclusion and paramonotone equilibrium problem

Yali Zhao; Qixin Dong; Xiaoqing Huang; Yali Zhao; Qixin Dong; Xiaoqing Huang

doi:10.3934/math.2025208

AIMS Mathematics

2025, Volume 10, Issue 2: 4504-4523. doi: 10.3934/math.2025208

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Research article

A self-adaptive viscosity-type inertial algorithm for common solutions of generalized split variational inclusion and paramonotone equilibrium problem

School of Mathematical Science, Bohai University, Jinzhou, Liaoning 121013, China

Received: 19 November 2024 Revised: 18 February 2025 Accepted: 21 February 2025 Published: 28 February 2025
MSC : 90C33, 49J52

In this paper, we aimed to consider the common elements of the generalized split variational inclusion and paramonotone equilibrium problem in real Hilbert spaces. Based on the self-adaptive method, a self-adaptive viscosity-type inertial algorithm to solve the problem under consideration was introduced and the inertial technique was used to accelerate the convergence rate of the method. Under the assumption of generalized monotonicity of the related mappings, the strong convergence of the iterative algorithm was established. The results presented here improve and generalize many results in this area.
- generalized split variational inclusion,
- equilibrium problem,
- paramonotonicity,
- strong convergence
Citation: Yali Zhao, Qixin Dong, Xiaoqing Huang. A self-adaptive viscosity-type inertial algorithm for common solutions of generalized split variational inclusion and paramonotone equilibrium problem[J]. AIMS Mathematics, 2025, 10(2): 4504-4523. doi: 10.3934/math.2025208

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Abstract

In this paper, we aimed to consider the common elements of the generalized split variational inclusion and paramonotone equilibrium problem in real Hilbert spaces. Based on the self-adaptive method, a self-adaptive viscosity-type inertial algorithm to solve the problem under consideration was introduced and the inertial technique was used to accelerate the convergence rate of the method. Under the assumption of generalized monotonicity of the related mappings, the strong convergence of the iterative algorithm was established. The results presented here improve and generalize many results in this area.

References

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