A Fixed-Component Point Theorem and Applications

  • Phan Quoc Khanh
  • Nguyen Hong QuanEmail author


We prove a topologically based characterization of the existence of fixed-component points for an arbitrary family of set-valued maps defined on a product set by using topologically based structures, without linear or convexity structures. Then, applying this general result, we derive sufficient conditions for the existence of coincidence-component points of families of set-valued maps and intersection points of families of sets, as examples for many other important points in nonlinear analysis. Applications to systems of variational relations and abstract economies are provided as examples for other optimization-related problems.


Fixed-component points Coincidence-component points Intersection points Maximal elements KKM-structures Optimization-related problems 

Mathematics Subject Classification

54H25 91A06 91A10 49J53 



This work was supported by the National Foundation for Science and Technology Development (NAFOSTED) of Vietnam under the Grant 101.01-2017.25. The work of the second author was completed during a stay at the Vietnam Institute for Advanced Study in Mathematics (VIASM), whose hospitality is gratefully acknowledged. The authors are very grateful to the anonymous referees for their valuable remarks and suggestions.


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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2017

Authors and Affiliations

  1. 1.Department of Mathematics, International UniversityVietnam National University Hochiminh CityHochiminh CityVietnam
  2. 2.Department of Scientific FundamentalsPosts and Telecommunications Institute of TechnologyHochiminh CityVietnam

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