39 research outputs found
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