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An additive functional inequality

신동윤|박춘길|이성진
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2014.06|한국수학논문집 (Korean Journal of Mathematics)|제22권 제2호|pp. 317-323|DOI http://dx.doi.org/10.11568/kjm.2014.22.2.317

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키워드

Hyers-Ulam stabilityfunctional inequalityJordan-von Neumann functional equation
주제분류수학

초록

In this paper, we solve the additive functional inequality (formula) where s is a nonzero real number and rho is a real number with |rho| < 3. Moreover, we prove the Hyers-Ulam stability of the above additive functional inequality in Banach spaces.

Abstract

In this paper, we solve the additive functional inequality (formula) where s is a nonzero real number and rho is a real number with |rho| < 3. Moreover, we prove the Hyers-Ulam stability of the above additive functional inequality in Banach spaces.

참고문헌 (12)

  1. T. Aoki, "On the stability of the linear transformation in Banach spaces", J. Math. Soc. Japan, 2, pp.64~66 (1950)
  2. P. W. Cholewa, "Remarks on the stability of functional equations", Aequationes Math, 27, pp.76~86 (1984)
  3. W. Fechner, "Stability of a functional inequalities associated with the Jordan-von Neumann functional equation", Aequationes Math, 71, pp.149~161 (2006)
  4. P. Gavruta, "A generalization of the Hyers-Ulam-Rassias stability of approxi-mately additive mappings", J. Math. Anal. Appl, 184, pp.431~436 (1994)
  5. A. Gilanyi, "Eine zur Parallelogrammgleichung aquivalente Ungleichung", Aequationes Math, 62, pp.303~309 (2001)
  6. A. Gilanyi, "On a problem by K. Nikodem", Math. Inequal. Appl, 5, pp.707~710 (2002)
  7. D. H. Hyers, "On the stability of the linear functional equation", Proc. Natl. Acad. Sci. U.S.A, 27, pp.222~224 (1941)
  8. C. Park, "Functional inequalities associated with Jordan-von Neumann-type additive functional equations", J. Inequal. Appl (2007)
  9. Th. M. Rassias, "On the stability of the linear mapping in Banach spaces", Proc. Amer. Math. Soc, 72, pp.297~300 (1978)
  10. J. Ratz, "On inequalities associated with the Jordan-von Neumann functional equation", Aequationes Math, 66, pp.191~200 (2003)
  11. F. Skof, "Propriet locali e approssimazione di operatori", Rend. Sem. Mat. Fis. Milano, 53, pp.113~129 (1983)
  12. S. M. Ulam, "A Collection of the Mathematical Problems" (1960), Interscience Publ

관련 논문AI추천

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