Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지
DOI QR코드

DOI QR Code

APPROXIMATE ADDITIVE-QUADRATIC MAPPINGS AND BI-JENSEN MAPPINGS IN 2-BANACH SPACES

  • Park, Won-Gil (Department of Mathematics Education Mokwon University)
  • Received : 2017.10.18
  • Accepted : 2017.10.23
  • Published : 2017.11.15
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we obtain the stability of the additive-quadratic functional equation f(x+y, z+w)+f(x+y, z-w) = 2f(x, z)+2f(x, w)+2f(y, z)+2f(y, w) and the bi-Jensen functional equation $$4f(\frac{x+y}{2},\;\frac{z+w}{2})=f(x,\;z)+f(x,\;w)+f(y,\;z)+f(y,\;w)$$ in 2-Banach spaces.

Keywords

References

  1. J.-H. Bae and W.-G. Park, On the solution of a bi-Jensen functional equation and its stability, Bull Korean Math. Soc. 43 (2006), 499-507. https://doi.org/10.4134/BKMS.2006.43.3.499
  2. H.-Y. Chu, A. Kim, and J. Park, On the Hyers-Ulam stabilities of functional equations on n-Banach spaces, Math. Nachr. 289 (2016), 1177-1188. https://doi.org/10.1002/mana.201400345
  3. H.-Y. Chu, J.-S. Park, and S. K. Yoo, A remark on a stability in multi-valued dynamics, J. Chungcheong Math. Soc. 30 (2017), 141-149.
  4. S. Gahler, 2-metrische Raume und ihre topologische Struktur, Math. Nachr. 26 (1963), 115-148. https://doi.org/10.1002/mana.19630260109
  5. S. Gahler, Lineare 2-normierte Raumen, Math. Nachr. 28 (1964), 1-43. https://doi.org/10.1002/mana.19640280102
  6. H.-M. Kim and H. M. Liang, Generalized quadratic functional equation with several variables and its Hyers-Ulam stability, J. Chungcheong Math. Soc. 29 (2016), 83-93. https://doi.org/10.14403/jcms.2016.29.1.83
  7. W.-G. Park, Approximate additive mappings in 2-Banach spaces and related topics, J. Math. Anal. Appl. 376 (2011), 193-202. https://doi.org/10.1016/j.jmaa.2010.10.004
  8. W.-G. Park, J.-H. Bae, and B.-H. Chung, On an additive quadratic functional equation and its stability, J. Appl. Math. & Computing, 18 (2005), 563-572.
  9. W.-G. Park and J.-H. Bae, On a Cauchy-Jensen functional equation and its stability, J. Math. Anal. Appl. 323 (2006), 634-645. https://doi.org/10.1016/j.jmaa.2005.09.028
  10. S. M. Ulam, A Collection of Mathematical Problems, Interscience Publishers, New York, 1960.