Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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SUPERSTABILITY OF THE GENERALIZED PEXIDER TYPE EXPONENTIAL EQUATION IN ABELIAN GROUP

  • Received : 2012.03.17
  • Accepted : 2012.06.15
  • Published : 2012.06.30
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Abstract

In this paper, we will prove the superstability of the following generalized Pexider type exponential equation $${f(x+y)}^m=g(x)h(y)$$, where $f,g,h\;:\;G{\rightarrow}\mathbb{R}$ are unknown mappings and $m$ is a fixed positive integer. Here G is an Abelian group (G, +), and $\mathbb{R}$ the set of real numbers. Also we will extend the obtained results to the Banach algebra. The obtained results are generalizations of P. G$\check{a}$vruta's result in 1994 and G. H. Kim's results in 2011.

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References

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