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Superstability and Stability of (r,s,t)-J*-Homomorphisms: Fixed Point and Direct Methods
Farhadabadi, Shahrokh,Park, Choonkil,Shin, Dong Yun Eudoxus Press LLC 2016 Journal of computational analysis and applications Vol.20 No.1
<P>In this paper, we introduce the following useful functional equations: f(x + y) f(x - 2y) + f (y - x) = f(x), (0.1) f(Sigma(p)(i=1) x(i)/p - 1) + Sigma(p)(i=2) f (Sigma(p)(j=1j not equal 1) x(j) - px(i)/p - 1) + f(Sigma(p)(i=2) x(i)-x(1)/p - 1) = f(x(1)) (0.2) and prove the superstability and the Hyers-Ulam stability of (r,s,t)-J*-homomorphisms, associated with those, by using the fixed point method and the direct method.</P>
Shin, D.Y.,Park, C.,Farhadabadi, S. Eudoxus Press LLC 2014 Journal of computational analysis and applications Vol.17 No.4
In this paper, we prove the Hyers-Ulam stability of ternary Jordan C*-homomorphisms and ternary Jordan C*-derivations associated with the following generalized Cauchy-Jensen functional equation:(p)Sigma(i)=f (1/k (p)Sigma(j=1j not equal 1) x(j) + x(i)) = p + k - 1/k (p)Sigma(i=1) f(x(i))by proving the generalization of Gavruta's theorem.