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

  • Aram V. Arutyunov
  • Evgeny S. Zhukovskiy
  • Sergey E. ZhukovskiyEmail author


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.


Partially ordered space Caristi-like condition Coincidence point Orderly covering mapping 

Mathematics Subject Classification

06A06 65K10 



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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Peoples’ Friendship University of RussiaMoscowRussia
  2. 2.Institute for Information Transmission Problem of the Russian Academy of Sciences (Kharkevich Institute)MoscowRussia
  3. 3.Faculty of Computational Mathematics and CyberneticsMoscow State UniversityMoscowRussia
  4. 4.Tambov State University named after G.R. DerzhavinTambovRussia
  5. 5.Moscow Institute of Physics and TechnologyDolgoprudny, Moscow regionRussia

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