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Caristi-Like Condition and the Existence of Minima of Mappings in Partially Ordered Spaces

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Abstract

In this paper, we study mappings acting in partially ordered spaces. For these mappings, we introduce a condition, analogous to the Caristi-like condition, used for functions defined on metric spaces. A proposition on the achievement of a minimal point by a mapping of partially ordered spaces is proved. It is shown that a known result on the existence of the minimum of a lower semicontinuous function defined on a complete metric space follows from the obtained proposition. New results on coincidence points of mappings of partially ordered spaces are obtained.

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Acknowledgements

The publication was supported by a grant from the Russian Science Foundation (Project No. 17-11-01168). Authors are grateful to anonymous referees for useful comments and remarks.

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Authors and Affiliations

  1. Peoples’ Friendship University of Russia, Moscow, Russia

    Aram V. Arutyunov & Sergey E. Zhukovskiy

  2. Institute for Information Transmission Problem of the Russian Academy of Sciences (Kharkevich Institute), Moscow, Russia

    Aram V. Arutyunov

  3. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia

    Aram V. Arutyunov

  4. Tambov State University named after G.R. Derzhavin, Tambov, Russia

    Evgeny S. Zhukovskiy

  5. Moscow Institute of Physics and Technology, Dolgoprudny, Moscow region, Russia

    Sergey E. Zhukovskiy

Authors
  1. Aram V. Arutyunov
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  2. Evgeny S. Zhukovskiy
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  3. Sergey E. Zhukovskiy
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Correspondence to Sergey E. Zhukovskiy.

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Arutyunov, A.V., Zhukovskiy, E.S. & Zhukovskiy, S.E. Caristi-Like Condition and the Existence of Minima of Mappings in Partially Ordered Spaces. J Optim Theory Appl 180, 48–61 (2019). https://doi.org/10.1007/s10957-018-1413-3

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  • DOI: https://doi.org/10.1007/s10957-018-1413-3

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