Károly Lajkó

On Measurable Functions Satisfying Multiplicative Type Functional Equations Almost Everywhere

Using the so-called “almost” variant of a well-known generalization of Steinhaus’ theorem, first we prove a general result on the multiplicative type functional equation (3), then we solve functional equations (1) and (2) originated from statistics under such conditions.

Sequenced problems for functional equations

There are many possible methods to solve equations of the form H(f(x + y), f(x − y), f(x), f(y), x, y) = 0 (x, y ∈ R), where H is a known function and f is the unknown function to be determined. Here we will create a sequence of problems for equations of type (1) (see on the next page). These sequenced problems are appropriate for the fostering of talented students on different level of mathematical education.

On a Mikusiński—Jensen Functional Equation

The following Mikusinski-Jensen type functional equation is investigated. The main result states that if I is an open real interval, or more generally, if I is a convex subset of a linear space whose intersection with straight lines is an open segment, then the above equation is equivalent to the so called Jensen functional equation.