We present some theorems of stability, in the Hyers-UlamRassias sense, for functional equations of quadratic-type, extending the results from [2], [8], [16], [19] and [20]. There are used both the direct and the fixed point methods. 2000 Mathematics Subject Classification: 39B52, 39B62, 39B82, 47H09.

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.

This article deals with a class of nonlinear fractional differential equations, initial conditions, involving the Riemann–Liouville derivative order α∈(1,2). The main objectives are to obtain conditions for existence and uniqueness solutions (within appropriate spaces), analyze stabilities Ulam–Hyers Ulam–Hyers–Rassias types. In fact, different obtained based on analysis an associated integral ...

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).

we provide a continuous representation of quasi-concave mappings by their upper level sets. A possible motivation is the extension to quasi-concave mappings of a result by Ulam and Hyers, which states that every approximately convex mapping can be approximated by a convex mapping. Keyword: quasi-concave, upper level set AMS classification: 47N10

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

In the present paper, the Hyers-Ulam stability and also the superstability of double centralizers and multipliers on Banach algebras are established by using a fixed point method. With this method, the condition of without order on Banach algebras is no longer necessary.

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.