Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지
DOI QR코드

DOI QR Code

A SHORT NOTE ON THE HYERS-ULAM STABILITY IN MULTI-VALUED DYNAMICS

  • Chu, Hahng-Yun (Department of Mathematics Chungnam National University) ;
  • Yoo, Seung Ki (Department of Mathematics Chungnam National University)
  • Received : 2018.01.05
  • Accepted : 2018.01.20
  • Published : 2018.02.15
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we consider the Hyers-Ulam stability on multi-valued dynamics. For a generalized n-dimensional quadratic set-valued functional equation, we prove the Hyers-Ulam stability for the functional equation in multi-valued dynamics.

Keywords

References

  1. T. Aoki, On the stability of the linear transformation in the Banach space, J. Math. Soc. Jap. 2 (1950), 64-66.
  2. J. Brzdek, Stability of additivity and fixed point methods, Fixed Point Theory and Appl. 2013 2013:285, 9pages.
  3. J. Brzdek, Note on stability of the Cauchy equation - an answer to a problem of Th.M. Rassias, Carpathian Journal of Mathematics, 30 (2014), 47-54.
  4. C. Castaing and M. Valadier, Convex analysis and measurable multifunctions, Lec. Notes in Math. Springer, Berlin, 580, 1977.
  5. P. W. Cholewa, Remarks on the stability of functional equations, Aequationes Math. 27 (1984), 76-86.
  6. H.-Y. Chu, D. S. Kang, and Th. M. Rassias, On the stability of a mixed n-dimensional quadratic functional equation, Bull. Belg. Math. Soc. 15 (2008), 9-24.
  7. H.-Y. Chu, A. Kim, and J.-S. Park, On the Hyers-Ulam stabilities of functional equations on n-Banach spaces, Math. Nachr. 289 (2016), 1177-1188.
  8. H.-Y. Chu, A. Kim, and S. K. Yoo, On the stability of generalized cubic set-valued functional equation, Appl. Math. Lett. 37 (2014), 7-14.
  9. H.-Y. Chu and S. K. Yoo, On the stability of an additive set-valued functional equation, J. Chungcheong Math. Soc. 27 (2014), 455-467.
  10. S. Czerwik, On the stability of the quadratic mapping in normed spaces, Abh. Math. Sem. Univ. Hamburg, 62 (1992), 59-64.
  11. P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), 431-436.
  12. D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. 27 (1941), 222-224.
  13. S.-M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis, Springer, New York, 2011.
  14. H. A. Kenary, H. Rezaei, Y. Gheisari, and C. Park, On the stability of set-valued functional equations with the fixed point alternative, Fixed Point Theory and Appl. 2012 2012:81, 17pages.
  15. G. Lu and C. Park, Hyers-Ulam stability of additive set-valued functional euqtions, Appl. Math. Lett. 24 (2011), 1312-1316.
  16. B. Margolis and J. B. Diaz, A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull. Amer. Math. Soc. 126 (1968), 305-309.
  17. C. Park, D. O'Regan and R. Saadati, Stability of some set-valued functional equations, Appl. Math. Lett. 24 (2011), 1910-1914.
  18. M. Piszczek, The properties of functional inclusions and Hyers-Ulam stability, Aequationes Math. 85 (2013), 111-118.
  19. M. Piszczek, On selections of set-valued inclusions in a single variable with applications to several variables, Results Math. 64 (2013), 1-12.
  20. H. Radstrom, An embedding theorem for spaces of convex sets, Proc. Amer. Math. Soc. 3 (1952), 165-169.
  21. J. M. Rassias, On appoximation of approximately linear mappings by linear mappings, J. Funct. Anal. 46 (1982), 126-130.
  22. Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.
  23. Th. M. Rassias, On the stability of the quadratic functional equation and its applications, Studia Univ. Babes-Bolyai, 43 (1998), 89-124.
  24. F. Skof, Proprieta locali e approssimazione di operatori, Rend. Semin. Mat. Fis. Milano, 53 (1983), 113-129.
  25. S. M. Ulam, A Collection of the Mathematical Problems, Interscience Publ. New York, 1960.