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Weak and strong convergence theorems for solving pseudo-monotone variational inequalities with non-Lipschitz mappings

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Abstract

The aim of this paper is to study a classical pseudo-monotone and non-Lipschitz continuous variational inequality problem in real Hilbert spaces. Weak and strong convergence theorems are presented under mild conditions. Our methods generalize and extend some related results in the literature and the main advantages of proposed algorithms there is no use of Lipschitz condition of the variational inequality associated mapping. Numerical illustrations in finite and infinite dimensional spaces illustrate the behaviors of the proposed schemes.

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Acknowledgments

The authors would like to thank Professor Aviv Gibali and two anonymous reviewers for their comments on the manuscript which helped us very much in improving and presenting the original 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, Zhejiang Normal University, Jinhua, 321004, People’s Republic of China

    Yekini Shehu

  3. Department of Mathematics, Computer Science and Information Systems, California University of Pennsylvania, Pennsylvania, PA, USA

    Olaniyi S. Iyiola

Authors
  1. Duong Viet Thong
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  2. Yekini Shehu
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  3. Olaniyi S. Iyiola
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Correspondence to Duong Viet Thong.

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Dedicated to Professor Le Dung Muu on the occasion of his 70th birthday

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Thong, D.V., Shehu, Y. & Iyiola, O.S. Weak and strong convergence theorems for solving pseudo-monotone variational inequalities with non-Lipschitz mappings. Numer Algor 84, 795–823 (2020). https://doi.org/10.1007/s11075-019-00780-0

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  • DOI: https://doi.org/10.1007/s11075-019-00780-0

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