On the uniqueness of continuous solutions of a functional equation of n-th order.
On the uniqueness of continuous solutions of functional equations
We consider the problem of the vanishing of non-negative continuous solutions ψ of the functional inequalities (1) ψ(f(x)) ≤ β(x,ψ(x)) and (2) α(x,ψ(x)) ≤ ψ(f(x)) ≤ β(x,ψ(x)), where x varies in a fixed real interval I. As a consequence we obtain some results on the uniqueness of continuous solutions φ :I → Y of the equation (3) φ(f(x)) = g(x,φ(x)), where Y denotes an arbitrary metric space.
On weighted Hardy and Poincaré-type inequalities for differences.
On -invariant measures and a functional equation
Oscillation of linear functional equations of higher order
The paper contains sufficient conditions under which all solutions of linear functional equations of the higher order are oscillatory.