Hlawka's functional inequality

The paper is devoted to the functional inequality (called by us Hlawka’s functional inequality) f(x + y) + f(y + z) + f(x + z) ≤ f(x + y + z) + f(x) + f(y) + f(z) for the unknown mapping f defined on an Abelian group, on a linear space or on the real line. The study of the foregoing inequality is motivated by Hlawka’s inequality: x + y + y + z + x + z ≤ x + y + z + x + y + z , which in particular holds true for all x, y, z from a real or complex inner product space

Inequalities characterizing linear-multiplicative functionals

We prove, in an elementary way, that if a nonconstant real-valued mapping defined on a real algebra with a unit satisfies certain inequalities, then it is a linear and multiplicative functional. Moreover, we determine all Jensen concave and supermultiplicative operators T : C(X) -> C(Y), where X and Y are compact Hausdorff spaces

Separation theorems for conditional functional equations

We prove two separation theorems for solutions of conditional Cauchy and Jensen equations

Some inequalities connected with the exponential function

summary:The paper is devoted to some functional inequalities related to the exponential mapping

On the Hyers–Ulam stability of functional equations connected with additive and quadratic mappings

AbstractWe investigate some inequalities connected with the Hyers–Ulam stability of three functional equations, which have a solution of the form φ=a+q, where a is an additive mapping and q is a quadratic one