The generalized Hyers–Ulam–Rassias stability of adjointable mappings on Hilbert C∗-modules are investigated. As a result, we get a solution for stability of the equation f(x)∗y = xg(y)∗ in the context of C∗-algebras. ∗2000 Mathematics Subject Classification. Primary 39B82, secondary 46L08, 47B48, 39B52 46L05, 16Wxx.

In this paper, the nonlinear stability of a functional equation in the setting of non-Archimedean normed spaces is proved. Furthermore, the interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean space, the and the theory of functional equations are also presented Key word: Hyers Ulam Rassias stability • cubic mappings • generalized normed space • Banach spac...

The generalized Hyers–Ulam–Rassias stability of adjointable mappings on Hilbert C∗-modules is investigated. As a corollary, we establish the stability of the equation f(x)∗y = xg(y)∗ in the context of C∗-algebras. We also prove that each approximately adjointable mapping is indeed adjointable.

In this paper, we obtain the general solution and the generalized Hyers-Ulam Rassias stability of the functional equation f(2x+ y) + f(2x− y) = 4(f(x+ y) + f(x− y))− 3 7 (f(2y)− 2f(y)) + 2f(2x) − 8f(x).

Using fixed point methods, we prove the generalized Hyers–Ulam–Rassias stability of ternary homomorphisms, and ternary multipliers in ternary Banach algebras for the Jensen–type functional equation f( x+ y + z 3 ) + f( x− 2y + z 3 ) + f( x+ y − 2z 3 ) = f(x) .

In this paper, we investigate the generalized Hyers–Ulam stability for the functional equation f(ax+y)+af(y−x)− a(a+ 1) 2 f(x)− a(a+ 1) 2 f(−x)− (a+1)f(y) = 0 in non-Archimedean normed spaces. Mathematics Subject Classification: 39B52, 39B82

A familiar functional equation f(ax+b) = cf(x) will be solved in the class of functions f : R → R. Applying this result we will investigate the Hyers-Ulam-Rassias stability problem of the generalized additive Cauchy equation f ( a1x1+···+amxm+x0 )= m ∑ i=1 bif ( ai1x1+···+aimxm ) in connection with the question of Rassias and Tabor.

Using the fixed point method, we establish a generalized Ulam Hyers stability result for the monomial functional equation in the setting of complete random p-normed spaces. As a particular case, we obtain a new stability theorem for monomial functional equations in β-normed spaces.