Problem 1.1. Given a metric group (G,Â·,d), a positive number Îµ, and a mapping f : Gâ†’ G which satisfies the inequality d( f (xy), f (x) f (y)) â‰¤ Îµ for all x, y âˆˆ G, do there exist an automorphism a ofâ€¦ (More)

We prove two general theorems, which appear to be very useful in investigation of the Hyers-Ulam stability of a higher order linear functional equation in single variable, with constant coefficients.â€¦ (More)

We prove that a set-valued map F : X â†’ P0(Y ) satisfying the functional inclusion F(x)â™¦F(y) âŠ† F(xâˆ— y) admits, in appropriate conditions, a unique selection f : X â†’ Y satisfying the functionalâ€¦ (More)