Hyers-Ulam-Rassias RNS Approximation of Euler-Lagrange-Type Additive Mappings
2012 ◽
Vol 2012
◽
pp. 1-15
◽
Keyword(s):
Recently the generalized Hyers-Ulam (or Hyers-Ulam-Rassias) stability of the following functional equation∑j=1mf(-rjxj+∑1≤i≤m,i≠jrixi)+2∑i=1mrif(xi)=mf(∑i=1mrixi)wherer1,…,rm∈R, proved in Banach modules over a unitalC*-algebra. It was shown that if∑i=1mri≠0,ri,rj≠0for some1≤i<j≤mand a mappingf:X→Ysatisfies the above mentioned functional equation then the mappingf:X→Yis Cauchy additive. In this paper we prove the Hyers-Ulam-Rassias stability of the above mentioned functional equation in random normed spaces (briefly RNS).
On the Stability of an -Variables Functional Equation in Random Normed Spaces via Fixed Point Method
2012 ◽
Vol 2012
◽
pp. 1-13
◽
Keyword(s):
Keyword(s):
2013 ◽
Vol 59
(2)
◽
pp. 299-320
Keyword(s):
2011 ◽
Vol 24
(12)
◽
pp. 2005-2009
◽
2011 ◽
Vol 403-408
◽
pp. 879-887