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Inertial projection methods for finding a minimum-norm solution of pseudomonotone variational inequality and fixed-point problems

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Abstract

In this work, we introduce two new iterative methods for finding the common element of the set of fixed points of a demicontractive mapping and the set of solutions of a pseudomonotone variational inequality problem in real Hilbert spaces. It is shown that the proposed algorithms converge strongly under mild conditions. The advantage of the proposed algorithms is that it does not require prior knowledge of the Lipschitz-type constants of the variational inequality mapping and only requires computing one projection onto a feasible set per iteration as well as without the sequentially weakly continuity of the variational inequality mapping. The novelty of the proposed algorithm may improve the efficiency of algorithms. Our results improve and extend some known results existing in the literature.

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Acknowledgements

The authors would like to thank the two referees for their valuable comments and suggestions which helped us very much in improving and presenting the original version of this paper.

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Authors and Affiliations

  1. Division of Applied Mathematics, Thu Dau Mot University, Thu Dau Mot, Binh Duong, Vietnam

    Duong Viet Thong

  2. Department of Mathematics, University of Science, Vietnam National University, 34 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam

    Vu Tien Dung

  3. Faculty of Mathematical Economics, National Economics University, Hanoi, Vietnam

    Luong Van Long

Authors
  1. Duong Viet Thong
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  2. Vu Tien Dung
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  3. Luong Van Long
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Correspondence to Duong Viet Thong.

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Communicated by Andreas Fischer.

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Cite this article

Thong, D.V., Dung, V.T. & Long, L.V. Inertial projection methods for finding a minimum-norm solution of pseudomonotone variational inequality and fixed-point problems. Comp. Appl. Math. 41, 254 (2022). https://doi.org/10.1007/s40314-022-01958-4

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  • DOI: https://doi.org/10.1007/s40314-022-01958-4

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