In this paper, using the fixed point and direct methods, we prove the generalized Hyers-Ulam-Rassias stability of the following Cauchy-Jensen additive functional equation: begin{equation}label{main} fleft(frac{x+y+z}{2}right)+fleft(frac{x-y+z}{2}right)=f(x)+f(z)end{equation} in various normed spaces. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias’ stability theorem t...

The mapping of an n-dimensional uniform dependence algorithm onto a linear processor array can be considered as a linear transformation problem. However, to find a linear space-optimal transformation is difficult because the conditions for checking a correct mapping and the space cost function do not have closed-form expressions, especially when the index set J of an n-dimensional algorithm is ...

Let X and Y be Hilbert C *-modules over a C *-algebra, and ϕ : X × Y → [0, ∞) be a function. A (not necessarily linear) mapping f : X → Y is called a ϕ-perturbed adjointable mapping if there exists a (not necessarily linear) mapping g : Y → X such that In this paper, we investigate the stability of adjointable mappings on Hilbert C *-modules and discuss the case where the modules are self-dual....

Consider two finite-dimensional normed spaces X and Y , a fixed convex cone K ⊂ X, and a linear mapping A : X → Y . We call A well-posed if AK = Y . In particular, in the purely linear case K = X, well-posedness coincides with surjectivity. Our interest is in the “distance to ill-posedness”: that is, we seek the smallest structured linear perturbation ∆A : X → Y such that the perturbed mapping ...

In this paper we study absolutely summing mappings on Banach spaces by exploring the cotype of their domains and ranges. It is proved that every n-linear mapping from L∞-spaces into K is (2; 2, ..., 2,∞)-summing and also shown that every n-linear mapping from L∞-spaces into F is (q; 2, ..., 2)-summing whenever F has cotype q. We also give new examples of analytic summing mappings and polynomial...