대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제46권2호
  • /
  • Pages.199-207
  • /
  • 2009
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

THE NEARLY ADDITIVE MAPS

  • 발행 : 2009.03.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

This note is a verification on the relations between almost linear and nearly additive maps; and the continuity of almost multiplicative nearly additive maps. Also we consider the stability of nearly additive and almost linear maps.

키워드

참고문헌

  1. E. Ansari-Piri, A class of factorable topological algebras, Proc. Edinburgh Math. Soc.(2) 33 (1990), no. 1, 53–59 https://doi.org/10.1017/S001309150002887X
  2. E. Ansari-Piri, Topics on fundamental topological algebras, Honam Math. J. 23 (2001), no. 1, 59–66
  3. E. Ansari-Piri, A note on star topological algebras, Honam Math. J. 27 (2005), no. 1, 77–82
  4. C. Baak and M. S. Moslehian, On the stability of $J^\ast$-homomorphisms, Nonlinear Anal. 63 (2005), no. 1, 42–48 https://doi.org/10.1016/j.na.2005.04.004
  5. Z. Gajda, On stability of additive mappings, Internat. J. Math. Math. Sci. 14 (1991), no. 3, 431–434 https://doi.org/10.1155/S016117129100056X
  6. P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), no. 3, 431–436 https://doi.org/10.1006/jmaa.1994.1211
  7. R. B. Holmes, Geometric Functional Analysis and Its Applications, Graduate Texts in Mathematics, No. 24. Springer-Verlag, New York-Heidelberg, 1975
  8. 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
  9. D. H. Hyers, G. Isac, and Th. M. Rassias, Stability of Functional Equations in Several Variables, Birkhauser, Basel, 1998
  10. D. H. Hyers and Th. M. Rassias, Approximate homomorphisms, Aequationes Math. 44 (1992), no. 2-3, 125–153 https://doi.org/10.1007/BF01830975
  11. K. Jarosz, Perturbations of Banach Algebras, Lecture Notes in Mathematics, 1120. Springer-Verlag, Berlin, 1985

피인용 문헌

  1. AUTOMATIC CONTINUITY OF ALMOST MULTIPLICATIVE LINEAR FUNCTIONALS ON FRÉCHET ALGEBRAS vol.53, pp.3, 2016, https://doi.org/10.4134/BKMS.b140116