Inertial subgradient extragradient with projection method for solving variational inequality and fixed point problems

Rose Maluleka; Godwin Chidi Ugwunnadi; Maggie Aphane; Rose Maluleka; Godwin Chidi Ugwunnadi; Maggie Aphane

doi:10.3934/math.20231539

AIMS Mathematics

2023, Volume 8, Issue 12: 30102-30119. doi: 10.3934/math.20231539

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Inertial subgradient extragradient with projection method for solving variational inequality and fixed point problems

1.
Department of Mathematics and Applied Mathematics, Sefako Makgato Health Science University, P.O. Box 94, Pretoria 0204, South Africa
2.
Department of Mathematics, University of Eswatini, Private 4, Kwaluseni M201, Eswatini

Received: 27 August 2023 Revised: 10 October 2023 Accepted: 13 October 2023 Published: 06 November 2023
MSC : 47H09, 47J25

In this paper, we introduce a new modified inertial Mann-type method that combines the subgradient extragradient method with the projection contraction method for solving quasimonotone variational inequality problems and fixed point problems in real Hilbert spaces. We establish strong convergence of the proposed method under some mild conditions without knowledge of the operator norm. Finally, we give numerical experiments to illustrate the efficiency of the method over the existing one in the literature.
- fixed point,
- quasimonotone operator,
- variational inequality problem,
- demimetric mapping,
- strong convergence
Citation: Rose Maluleka, Godwin Chidi Ugwunnadi, Maggie Aphane. Inertial subgradient extragradient with projection method for solving variational inequality and fixed point problems[J]. AIMS Mathematics, 2023, 8(12): 30102-30119. doi: 10.3934/math.20231539

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Abstract

In this paper, we introduce a new modified inertial Mann-type method that combines the subgradient extragradient method with the projection contraction method for solving quasimonotone variational inequality problems and fixed point problems in real Hilbert spaces. We establish strong convergence of the proposed method under some mild conditions without knowledge of the operator norm. Finally, we give numerical experiments to illustrate the efficiency of the method over the existing one in the literature.

References

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