Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (2): 266-273.

• Articles • Previous Articles     Next Articles

Stability of Cubic Functional Equations in Banach Spaces

 CHENG Li-Hua1, LIAN Tie-Yan2   

  1. 1.College Science, Xian Polytechnic University, Xi'an 710048|2.College Science, Shanxi University of Science &|Technology, Xi'an 710021
  • Received:2012-10-08 Revised:2013-04-06 Online:2014-04-25 Published:2014-04-25
  • Supported by:

    陕西省教育厅自然科学专项基金(12jk0879)资助.

Abstract:

In this note, we will find out the general solution and investigate the Hyers-Ulam-Rassias stability of a cubic functional equation af(x+ay)-f(ax+y)=a(a2-1)/2[f(x+y)+f(x-y)]+(a4-1)f(y)-2a(a2-1)f(x), in Banach spaces for a fixed integer a with a≠0, ±1. Forthermore, we give the equivalent proof of eight functional equations. At last, the stability of cubic functional equation in Banach spaces is dissucied.

Key words: Stability, Cubic equation, Jordan homorphism

CLC Number: 

  • 39B52
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