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Extragradient methods for solving non-Lipschitzian pseudo-monotone variational inequalities

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Abstract

The purpose of this paper is to study and analyze two new extragradient methods for solving non-Lipschitzian and pseudo-monotone variational inequalities in real Hilbert spaces. Under suitable conditions, weak and strong convergence theorems of the proposed methods are established. We present academic and numerical examples for illustrating the behavior of the proposed algorithms.

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Acknowledgements

The authors would like to thank Professor Simeon Reich and the referees for their comments on the manuscript which helped in improving earlier version of this paper.

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Authors and Affiliations

  1. Applied Analysis Research Group Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Duong Viet Thong

  2. Department of Mathematics, ORT Braude College, 2161002, Karmiel, Israel

    Aviv Gibali

  3. The Center for Mathematics and Scientific Computation, University of Haifa, Mt. Carmel, 3498838, Haifa, Israel

    Aviv Gibali

Authors
  1. Duong Viet Thong
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  2. Aviv Gibali
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Correspondence to Duong Viet Thong.

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Thong, D.V., Gibali, A. Extragradient methods for solving non-Lipschitzian pseudo-monotone variational inequalities. J. Fixed Point Theory Appl. 21, 20 (2019). https://doi.org/10.1007/s11784-018-0656-9

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