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Acta Mathematica Sinica, English Series

, Volume 25, Issue 1, pp 29–38 | Cite as

On the stability of the generalized sine functional equations

  • Gwang Hui Kim
Article

Abstract

The aim of this paper is to study the stability problem of the generalized sine functional equations as follows:
$$ \begin{array}{*{20}c} {g(x)f(y) = f\left( {\frac{{x + y}} {2}} \right)^2 - f\left( {\frac{{x - y}} {2}} \right)^2 ,} \\ {f(x)g(y) = f\left( {\frac{{x + y}} {2}} \right)^2 - f\left( {\frac{{x - y}} {2}} \right)^2 ,} \\ {g(x)g(y) = f\left( {\frac{{x + y}} {2}} \right)^2 - f\left( {\frac{{x - y}} {2}} \right)^2 .} \\ \end{array} $$
.

Namely, we have generalized the Hyers-Ulam stability of the (pexiderized) sine functional equation.

Keywords

stability superstability sine functional equation cosine functional equation 

MR(2000) Subject Classification

39B82 39B62 39B52 

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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 GmbH 2009

Authors and Affiliations

  1. 1.Department of Applied MathematicsKangnam UniversityYongin, GyeonggiKorea

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