Acta mathematica scientia,Series B ›› 2012, Vol. 32 ›› Issue (6): 2247-2258.doi: 10.1016/S0252-9602(12)60174-X

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APPROXIMATION OF A CAUCHY-JENSEN ADDITIVE FUNCTIONAL EQUATION IN NON-ARCHIMEDEAN NORMED SPACES

Hassan Azadi Kenary   

  1. Department of Mathematics, College of Sciences, Yasouj University, Yasouj 75914-353, Iran
  • Received:2011-05-24 Revised:2011-12-31 Online:2012-11-20 Published:2012-11-20

Abstract:

Using the fixed point and direct methods, we prove the Hyers-Ulam stability of the following Cauchy-Jensen additive functional equation
2f(∑pi=1xi +∑qj=1yj + 2∑dk=1zk/2) =2f(∑pi=1xi +∑qj=1yj + 2∑dk=1(zk),

where p, q, d are integers greater than 1, in non-Archimedean normed spaces.

Key words: Hyers-Ulam stability, Cauchy-Jensen additive functional equation, fixed point, non-Archimedean normed spaces

CLC Number: 

  • 39B52
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