J4 ›› 2013, Vol. 48 ›› Issue (4): 1-4.

• Articles •     Next Articles

On the Hyers-Ulam Stability of n-cocycles

JI Pei-sheng1, QI Wei-qing2, LIU Rong-rong1   

  1. 1. College of Mathematics, Qingdao University, Qingdao 266071, Shandong, China;
    2. College of Information Engineering, Qingdao University, Qingdao 266071, Shandong, China
  • Received:2012-10-22 Online:2013-04-20 Published:2013-04-16

Abstract:

Let A be a Banach algebra and M be a Banach A-module. An n-linear mapping f: An→M from An into M is called an n-cocycle if it satisfies that x1f(x1,…,xn+1)+(-1)n+1f(x1,…,xn)xn+1+∑ni=1(-1)if(x1,…,xi-1,xixi+1,xi+2,…,xn+1)=0 for all x1,…,xn+1∈A.It is proved that the n-cocycles from An into M are Hyers-Ulam stable.

Key words:  Banach algebra; n-cocycle; Hyers-Ulam stability

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