대한수학회보 (Bulletin of the Korean Mathematical Society)

대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

HYERS-ULAM-RASSIAS STABILITY OF A QUADRATIC FUNCTIONAL EQUATION

  • Trif, Tiberiu (Universitatea Babes-Bolyai, Facultatea de Matematica si Informatica)
  • 발행 : 2003.05.01

초록

In this paper we deal With the quadratic functional equation (equation omitted) deriving from an inequality of T. Popoviciu for convex functions. We solve this functional equation by proving that its solutions we the polynomials of degree at most two. Likewise, we investigate its stability in the spirit of Hyers, Ulam, and Rassias.

키워드

파일

원문 PDF 다운로드

참고문헌

  1. Functional equations in several variables J.Aczel;J.Dhombres
  2. Aequationes Math. v.27 Remarks on the stability of functional equations P.W.Cholewa https://doi.org/10.1007/BF02192660
  3. Seminaire de la theorie de la meilleure approxomation, convexite et optimisation On some functional equations deriving from the inequality of Tiberiu Popoviciu for convex functions B.Crstici;E.Popoviciu(ed.)
  4. Abh. Math. Sem. Univ. Hamburg v.62 On the stability of the quadratic mapping in normed spaces S.Czerwik https://doi.org/10.1007/BF02941618
  5. Int. J. Math. Math. Sci. v.14 On stability of additive mappings Z.Gajda https://doi.org/10.1155/S016117129100056X
  6. Proc. Nat. Acad. Sci. U.S.A. v.27 On the stability of the linear functional equation D.H.Hyers https://doi.org/10.1073/pnas.27.4.222
  7. Stability of funcational equations in several variables D.H.Hyers;G.Isac;Th.M.Rassias
  8. Aequationes Math. v.44 Approximate homomorphisms D.H.Hyers;Th.M.Rassias https://doi.org/10.1007/BF01830975
  9. J. Math. Anal. Appl. v.222 On the Hyers-Ulam stability of the functional equations that have the quadratic property S.M.Jung https://doi.org/10.1006/jmaa.1998.5916
  10. J. Math. Anal. Appl. v.232 On the Hyers-Ulam-Rassias stability of a quadratic functional equation S.M.Jung https://doi.org/10.1006/jmaa.1999.6282
  11. J. Math. Anal. Appl. v.270 On the stability of a quadratic Jensen type functional equation Y.W.Lee https://doi.org/10.1016/S0022-247X(02)00093-8
  12. An. Stiint. Univ. Al. I. Cuza Iasi Sect. Ia Mat. v.11 Sur certaines inegalites qui caracterisent les fonctions convexes T.Popoviciu
  13. Proc. Amer. Math. Soc. v.72 On the stability of the linear mapping in Banach spaces Th.M.Rassias https://doi.org/10.1090/S0002-9939-1978-0507327-1
  14. J. Math. Anal. Appl. v.173 On the Hyers-Ulam stability of linear mappings Th.M.Rassias;P.Semrl https://doi.org/10.1006/jmaa.1993.1070
  15. J. Math. Anal. Appl. v.250 Hyers-Ulam-Rassias stability of a Jensen type functional equation T.Trif https://doi.org/10.1006/jmaa.2000.6995
  16. Nonlinear Funct. Anal. Appl. v.7 A generalization of the Hyers-Ulam-Rassias stability of the Popoviciu functional equation T.Trif
  17. J. Math. Anal. Appl. v.272 On the stability of a functional equation deriving from an inequality of Popoviciu for convex functions T.Trif https://doi.org/10.1016/S0022-247X(02)00181-6
  18. Problems in modern mathematics S.M.Ulam

피인용 문헌

  1. Popoviciu Type Equations on Cylinders vol.67, pp.3-4, 2015, https://doi.org/10.1007/s00025-015-0440-8
  2. Stability Problem for Jensen–type Functional Equations of Cubic Mappings vol.22, pp.6, 2006, https://doi.org/10.1007/s10114-005-0736-9
  3. On extension of the solutions of the Popoviciu type equations on groups vol.147, pp.2, 2015, https://doi.org/10.1007/s10474-015-0512-y
  4. STABILITY OF A MIXED TYPE FUNCTIONAL EQUATION IN 3-VARIABLES vol.29, pp.4, 2007, https://doi.org/10.5831/HMJ.2007.29.4.543