Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
권호 표지
DOI QR코드

DOI QR Code

Approximation of Pompeiu's Point

  • Received : 2016.04.12
  • Accepted : 2016.06.07
  • Published : 2017.06.23
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we obtain the refined stability of Pompeiu's points which extends a result of Huang and Li [8].

Keywords

References

  1. T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, 2(1950), 64-66. https://doi.org/10.2969/jmsj/00210064
  2. D. G. Bourgin, Classes of transformations and bordering transformations, Bull. Amer. Math. Soc., 57(1951), 223-237. https://doi.org/10.1090/S0002-9904-1951-09511-7
  3. Y. J. Cho, T. M. Rassias, R. Saadati, Stability of Functional Equations in Random Normed Spaces, Springer Optimization and Its Applications, 86, Springer, New York, 2013.
  4. S. Czerwik, Stability of Functional Equations of Ulam-Hyers-Rassias Type, Hadronic Press, Florida, 2003.
  5. M. Das, T. Riedel, P. K. Sahoo, Hyers-Ulam stability of Flett's points, Appl. Math. Lett., 16(2003), 269-271. https://doi.org/10.1016/S0893-9659(03)80042-3
  6. T. M. Flett, A mean value theorem, Math. Gazette, 42(1958), 38-39. https://doi.org/10.1017/S0025557200236267
  7. P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184(1994), 431-436 https://doi.org/10.1006/jmaa.1994.1211
  8. J. Huang, Y. Li, Hyers-Ulam stability of Pompeiu's point, Kyungpook Math. J., 55(2015), 103-107. https://doi.org/10.5666/KMJ.2015.55.1.103
  9. D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U. S. A., 27(1941), 222-224. https://doi.org/10.1073/pnas.27.4.222
  10. D. H. Hyers, S. M. Ulam, On the stability of differential expressions, Math. Mag., 28(1954), 59-64. https://doi.org/10.2307/3029365
  11. S. -M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis, Springer Optimization and Its Applications, 48, Springer, New York, 2011.
  12. H. -M. Kim, H. -Y. Shin, Approximation of almost Sahoo-Riedel's points by Sahoo-Riedel's points, Aequationes Math., 90(2016), 809815. https://doi.org/10.1007/s00010-015-0390-y
  13. W. Lee, S. Xu, F. Ye, Hyers-Ulam stability of Sahoo-Riedel's point, Appl. Math. Lett., 22(2009), 1649-1652. https://doi.org/10.1016/j.aml.2009.05.012
  14. T. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72(1978), 297-300. https://doi.org/10.1090/S0002-9939-1978-0507327-1
  15. T. M. Rassias, Functional Equations, Inequalities and Applications, Kluwer Academic Publishers, Dordrecht, London, 2003.
  16. S. M. Ulam, Problems in Modern Mathematics, Chapter 6, Wiley, New York 1964.