JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (02): 60-66.doi: 10.6040/j.issn.1671-9352.0.2014.349

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General solution and stability of bi-cubic functional equation

QI Wei-qing1, JI Pei-sheng2, LU Hai-ning2   

  1. 1. College of Information Engineering, Qingdao University, Qingdao 266071, Shandong China;
    2. College of Mathematics, Qingdao University, Qingdao 266071, Shandong China
  • Received:2014-07-31 Revised:2014-11-03 Online:2015-02-20 Published:2015-01-27

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Abstract: Let X and Y be real vector spaces. A mapping f:X2→Y is called bi-cubic if it satisfies f(2x1+x2,2y1+y2)+f(2x1+x2,2y1-y2)+f(2x1-x2,2y1+y2)+ f(2x1-x2,2y1-y2)=4f(x1+x2,y1+y2)+4f(x1-x2,y1+y2)+24f(x1,y1+y2)+ 4f(x1+x2,y1-y2)+4f(x1-x2,y1-y2)+24f(x1,y1-y2)+24f(x1+x2,y1)+ 24f(x1-x2,y1)+144f(x1,y1) for all x1,x2,y1,y2∈X. The solution of this equation is obtained and the Hyers-Ulam stability of it is proved on fuzzy Banach spaces.

Key words: Hyers-Ulam stability, cubic functional equation, bi-cubic functional equation, fuzzy Banach space

CLC Number: 

  • O177.1
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