• Title/Summary/Keyword: Additive functional equation

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ON THE STABILITY OF A GENERALIZED ADDITIVE FUNCTIONAL EQUATION II

  • Lee, Jung-Rye;Lee, Tae-Keug;Shin, Dong-Yun
    • The Pure and Applied Mathematics
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    • v.14 no.2 s.36
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    • pp.111-125
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    • 2007
  • For an odd mapping, we study a generalized additive functional equation in Banach spaces and Banach modules over a $C^*-algebra$. And we obtain generalized solutions of a generalized additive functional equation and so generalize the Cauchy-Rassias stability.

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HYERS-ULAM STABILITY OF AN ADDITIVE TYPE FUNCTIONAL EQUATION

  • Lee, Don-O
    • Journal of applied mathematics & informatics
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    • v.13 no.1_2
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    • pp.471-477
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    • 2003
  • In this paper we invstigate the new additive type functional equation f(2x - y) + f(x-2y) = 3f(x)-3f(y) and prove the stability problem for this equation in the spirit of Hyers, Ulam, Rassias and Gavruta.

A GENERALIZED ADDITIVE-QUARTIC FUNCTIONAL EQUATION AND ITS STABILITY

  • HENGKRAWIT, CHARINTHIP;THANYACHAROEN, ANURK
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.6
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    • pp.1759-1776
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    • 2015
  • We determine the general solution of the generalized additive-quartic functional equation f(x + 3y) + f(x - 3y) + f(x + 2y) + f(x - 2y) + 22f(x) - 13 [f(x + y) + f(x - y)] + 24f(y) - 12f(2y) = 0 without assuming any regularity conditions on the unknown function f : ${\mathbb{R}}{\rightarrow}{\mathbb{R}}$ and its stability is investigated.

APPROXIMATE ADDITIVE MAPPINGS IN 2-BANACH SPACES AND RELATED TOPICS: REVISITED

  • YUN, SUNGSIK
    • Korean Journal of Mathematics
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    • v.23 no.3
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    • pp.393-399
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    • 2015
  • W. Park [J. Math. Anal. Appl. 376 (2011) 193-202] proved the Hyers-Ulam stability of the Cauchy functional equation, the Jensen functional equation and the quadratic functional equation in 2-Banach spaces. But there are serious problems in the control functions given in all theorems of the paper. In this paper, we correct the statements of these results and prove the corrected theorems. Moreover, we prove the superstability of the Cauchy functional equation, the Jensen functional equation and the quadratic functional equation in 2-Banach spaces under the original given conditions.