Acta Mathematica Sinica, English Series

, Volume 26, Issue 7, pp 1255–1262 | Cite as

Solution and stability of a cubic functional equation

  • Kil Woung Jun
  • Sang Baek Lee
  • Won Gil Park


In this paper, we investigate the general solution and the stability of a cubic functional equation
$$ f(x + ny) + f(x - ny) + f(nx) = n^2 f(x + y) + n^2 f(x - y) + (n^3 - 2n^2 + 2)f(x), $$
where n ≥ 2 is an integer. Furthermore, we prove the stability by the fixed point method.


Hyers-Ulam stability cubic functional equation alternative of fixed point 

MR(2000) Subject Classification

39B52 39B82 


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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of MathematicsChungnam National UniversityDaejeonSouth Korea
  2. 2.Department of Mathematics Education, College of EducationMokwon UniversityDaejeonSouth Korea

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