On the Hyers-Ulam stability of quadratic functional equations.
On the lower hull of convex functions.
On the stability of a functional equation related to associativity
On the stability of Drygas functional equation on groups.
On the support of midconvex operators.
On the support of midconvex operators. (Summary).
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.
Polynomial selections and separation by polynomials
K. Nikodem and the present author proved in [3] a theorem concerning separation by affine functions. Our purpose is to generalize that result for polynomials. As a consequence we obtain two theorems on separation of an n-convex function from an n-concave function by a polynomial of degree at most n and a stability result of Hyers-Ulam type for polynomials.
Quasi-additive functions.
Regularity properties of functional equations and inequalities.
Relative rearrangement and interpolation inequalities.
We prove here that the Poincaré-Sobolev pointwise inequalities for the relative rearrangement can be considered as the root of a great number of inequalities in various sets not necessarily vector spaces. In particular, new interpolation inequalities can be derived.
Remarks on stability of functional equations.
Remarks on the stability of functional equations.
Separation by monotonic functions.
Separation via quadratic functions.
Separation via quadratic functions. (Summary).