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Isotonicity of the metric projection with applications to variational inequalities and fixed point theory in Banach spaces

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Abstract

In this paper, we discuss isotonicity characterizations of the metric projection operator, including its necessary and sufficient conditions for isotonicity onto sublattices in Banach spaces. Then, we demonstrate their applications to variational inequalities and fixed point theory in Banach spaces. Our work generalizes many existing results obtained in earlier work.

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Acknowledgments

The authors were financially supported by the National Natural Science Foundation of China (11371221, 11571296).

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Authors and Affiliations

  1. College of Information Science and Engineering, Shandong Agricultural University, Taian, 271018, Shandong, China

    Dezhou Kong

  2. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, Shandong, China

    Lishan Liu

  3. Department of Mathematics and Statistics, Curtin University, Perth, WA, 6845, Australia

    Lishan Liu & Yonghong Wu

Authors
  1. Dezhou Kong
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  2. Lishan Liu
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  3. Yonghong Wu
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Correspondence to Lishan Liu.

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Kong, D., Liu, L. & Wu, Y. Isotonicity of the metric projection with applications to variational inequalities and fixed point theory in Banach spaces. J. Fixed Point Theory Appl. 19, 1889–1903 (2017). https://doi.org/10.1007/s11784-016-0337-5

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