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Iterative Algorithms for Pseudomonotone Variational Inequalities and Fixed Point Problems of Pseudocontractive Operators

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  • Yonghong Yao

    (School of Mathematical Sciences, Tiangong University, Tianjin 300387, China
    The Key Laboratory of Intelligent Information and Big Data Processing of NingXia Province, North Minzu University, Yinchuan 750021, China)

  • Mihai Postolache

    (Center for General Education, China Medical University, Taichung 40402, Taiwan
    Romanian Academy, Gh. Mihoc-C. Iacob Institute of Mathematical Statistics and Applied Mathematics, Bucharest 050711, Romania
    Department of Mathematics and Informatics, University “Politehnica” of Bucharest, Bucharest 060042, Romania)

  • Jen-Chih Yao

    (Center for General Education, China Medical University, Taichung 40402, Taiwan)

Abstract

In this paper, we are interested in the pseudomonotone variational inequalities and fixed point problem of pseudocontractive operators in Hilbert spaces. An iterative algorithm has been constructed for finding a common solution of the pseudomonotone variational inequalities and fixed point of pseudocontractive operators. Strong convergence analysis of the proposed procedure is given. Several related corollaries are included.

Suggested Citation

  • Yonghong Yao & Mihai Postolache & Jen-Chih Yao, 2019. "Iterative Algorithms for Pseudomonotone Variational Inequalities and Fixed Point Problems of Pseudocontractive Operators," Mathematics, MDPI, vol. 7(12), pages 1-13, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1189-:d:293964
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    References listed on IDEAS

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    3. Thakur, Balwant Singh & Thakur, Dipti & Postolache, Mihai, 2016. "A new iterative scheme for numerical reckoning fixed points of Suzuki’s generalized nonexpansive mappings," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 147-155.
    4. J. Bello Cruz & A. Iusem, 2010. "Convergence of direct methods for paramonotone variational inequalities," Computational Optimization and Applications, Springer, vol. 46(2), pages 247-263, June.
    5. Jun Yang & Hongwei Liu, 2018. "A Modified Projected Gradient Method for Monotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 197-211, October.
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