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

Author

Listed:
  • Aram V. Arutyunov

    (Peoples’ Friendship University of Russia
    Institute for Information Transmission Problem of the Russian Academy of Sciences (Kharkevich Institute)
    Moscow State University)

  • Evgeny S. Zhukovskiy

    (Tambov State University named after G.R. Derzhavin)

  • Sergey E. Zhukovskiy

    (Peoples’ Friendship University of Russia
    Moscow Institute of Physics and Technology)

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.

Suggested Citation

  • Aram V. Arutyunov & Evgeny S. Zhukovskiy & Sergey E. Zhukovskiy, 2019. "Caristi-Like Condition and the Existence of Minima of Mappings in Partially Ordered Spaces," Journal of Optimization Theory and Applications, Springer, vol. 180(1), pages 48-61, January.
    • Handle: RePEc:spr:joptap:v:180:y:2019:i:1:d:10.1007_s10957-018-1413-3
    DOI: 10.1007/s10957-018-1413-3
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