Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지
DOI QR코드

DOI QR Code

THE CHAIN RECURRENT SET ON COMPACT TVS-CONE METRIC SPACES

  • Received : 2019.10.10
  • Accepted : 2020.02.05
  • Published : 2020.02.15
Download PDF
⟨ Previous Next ⟩

Abstract

Conley introduced attracting sets and repelling sets for a flow on a topological space and showed that if f is a flow on a compact metric space, then 𝓡(f) = ⋂{AU ∪ A*U |U is a trapping region for f}. In this paper we introduce chain recurrent set, trapping region, attracting set and repelling set for a flow f on a TVS-cone metric space and prove that if f is a flow on a compact TVS-cone metric space, then 𝓡(f) = ⋂{AU ∪ A*U |U is a trapping region for f}.

Keywords

References

  1. Charles Conley, Isolated Invariant Sets and the Morse Index, American Mathematical Society, Providence, 1978.
  2. L. G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007) 1468-1476. https://doi.org/10.1016/j.jmaa.2005.03.087
  3. Shou Lin and Ying Ge, Compact-valued continuous relations on TVS-cone metric spaces, Published by Faculty of Sciences and Mathematics, University of Nis, Serbia, Filomat, 27 (2013), no. 2, 327-332.
  4. I. Beg, A. Azam, and M. Arshad, Common fixed points for maps on topological vector space valued cone metric spaces, Inter. J. Math. Math. Science, 2009, Article ID 560264, 8pages, doi:10.1155/2009/560264.