Fixed Points and Stability of an Additive Functional Equation of n‐Apollonius Type in C^∗‐Algebras

Abstract

Using the fixed point method, we prove the generalized Hyers-Ulam stability ofC∗-algebra homomorphisms and of generalized derivations onC∗-algebras for the following functional equation of Apollonius type∑i=1nf(z−xi)=−(1/n)∑1≤i<j≤nf(xi+xj)+nf(z−(1/n2)∑i=1nxi).

Generalized Hyers-Ulam stability for general additive functional equations on non-Archimedean random lie C*-algebras

“…Hence we have δ(xy) = δ(x)y + xδ(y) for all x, y ∈ A. This means that δ is a derivation satisfying (24). This completes the proof.…”

“…It follows from (6), (28) and 29 for all x, y ∈ A. Thus, δ : A → A is a Lie derivation satisfying (24), as desired.…”

Nonlinear approximation of an ACQ-functional equation in nan-spaces

“…The stability problems of several functional equations have been extensively investigated by a number of authors, and there are many interesting results concerning this problem (see [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]).…”

Hyers–Ulam–Rassias Stability of a Quadratic and Additive Functional Equation in Quasi-Banach Spaces

“…[1], [17]. Moradlou, Vaezi and Park [14] have investigated Hyers-Ulam-Rassias stability of an additive functional equation of n-Apollonius type in C * -algebras. Eskandani [7] have established the general solution and investigated the Hyers-Ulam-Rassias stability of an additive functional equation in quasi-Banach spaces.…”