Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지
DOI QR코드

DOI QR Code

ON THE STABILITY OF A GENERAL ADDITIVE FUNCTIONAL INEQUALITY IN BANACH SPACES

  • Received : 20130931
  • Accepted : 2013.10.30
  • Published : 2013.11.15
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we prove the generalized Hyers-Ulam stability of the additive functional inequality $${\parallel}f(2x_1)+f(2x_2)+{\cdots}+f(2x_n){\parallel}{\leq}{\parallel}tf(x_1+x_2+{\cdots}+x_n){\parallel}$$ in Banach spaces where a positive integer $n{\geq}3$ and a real number t such that 2${\leq}$t

Keywords

References

  1. D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. 27 (1941), 222-224. https://doi.org/10.1073/pnas.27.4.222
  2. J. R. Lee, C. Park, and D. Y. Shin, Stability of an additive functional inequality in proper CQ*-algebras, Bull. Korean Math. Soc. 48 (2011), 853-871. https://doi.org/10.4134/BKMS.2011.48.4.853
  3. C. Park, Y. S. Cho, and M. H. Han, Functional inequalities associated with Jordan-von Neumann-type additive functional equations, J. Inequal. Appl. 2007 (2007), Article ID 41820, 13 pages.
  4. S. M. Ulam, A Collection of the Mathematical Problems, Interscience Publ., New York, 1960.

Cited by

  1. STABILITY OF AN ADDITIVE FUNCTIONAL INEQUALITY IN BANACH SPACES vol.29, pp.1, 2016, https://doi.org/10.14403/jcms.2016.29.1.103