Anna Bahyrycz

On an equation characterizing multi-additive-quadratic mappings and its Hyers-Ulam stability

In this paper we unify the system of functional equations defining a multi-additive-quadratic mapping to obtain a single equation. We also prove, using the fixed point method, the generalized Hyers-Ulam stability of this equation thus generalizing some known results.

On solutions of the second generalization of d'Alembert's functional equation on a restricted domain

Let A be a subgroup of an abelian group (G,+) and P be a quadratically closed field with char P 2. We give a full description of all pairs of functions f:G->P,g:A->P satisfying the equation(a)f(x+y)+f(x-y)=2g(x)f(y)(x,y)@?AxG.We present an example of solution (f,g) of (a) that cannot be extended to a solution (f,[emailxa0protected]?) of the equation (b)f(x+y)+f(x-y)[emailxa0protected]?(x)f(y)x,[emailxa0protected]?G.

On an equation characterizing multi-cauchy-jensen mappings and its Hyers-Ulam stability

Abstract In this paper, we give two characterizations of multi-Cauchy-Jensen mappings. One of them reduces the system of n equations defining these mappings to a single functional equation. We also prove, using the fixed point method, the generalized Hyers-Ulam stability of this equation. Our results generalize some known outcomes.

On approximately (p, q)-wright affine functions and inner product spaces

Abstract We prove, using the fixed point approach, some results on hyperstability (in normed spaces) of the equation that defines the generalization of p-Wright affine functions and show that they yield a simple characterization of the complex inner product spaces.

Remarks on Stability of the Equation of Homomorphism for Square Symmetric Groupoids

Let ((G,star)) and ((H,circ)) be square symmetric groupoids and (Ssubset G) be nonempty. We present some remarks on stability of the following conditional equation of homomorphism n n

On stability of the general linear equation

f(xstar y)=f(x)circ f(y) qquad x,yin S, xstar yin S;,

Hyperstability of general linear functional equation

n nin the class of functions mapping S into H. In particular, we consider the situation where (H=mathbb{R}) and n n