Roman Badora

On approximate ring homomorphisms

We prove the stability of a generalization of the Bourgins result on approximate ring homomorphisms.

On Some Trigonometric Functional Inequalities

We deal with d’Alembert’s and Wilson’s differences

A note on a fixed point theorem and the Hyers–Ulam stability

f\left( {x + y} \right) + f\left( {x - y} \right) - 2f\left( x \right)f\left( y \right)

On the separation with n-additive functions

and

On a joint generalization of Cauchy's and d'Alembert's functional equations

f\left( x \right)f\left( y \right) - f{\left( {\frac{{x + y}}{2}} \right)^2} + f{\left( {\frac{{x - y}}{2}} \right)^2}

Decomposition of mappings approximately inner product preserving

respectively, assuming that their absolute values (or norms) are majorized by some function in a single variable. The superstability type results obtained are then used to characterize the functions