Karol Baron

On the Cauchy difference

SummaryAssume thatE andF are real topological vector spaces (which are assumed to be Hausdorff) and letK be a countable and discrete subgroup ofF. Supposef: E → F satisfies

Orthogonality and additivity modulo a subgroup

f(x + y) - f(x) - f(y) \in K

On functions having Cauchy differences in some prescribed sets

for allx, y ∈ E. Conditions are established under whichf has the formA + k, whereA: E →F is a continuous linear operator andk takes values inK only. For example, ifF is assumed to be locally convex and iff andE satisfy suitable conditions (such asE being a Baire space andf a Baire function) thenf has the formA + k, whereA : E →F is a continuous linear operator and k(E)

On the convergence of sequences of iterates of random-valued functions

k(E) \subseteq K

Recent results on functional equations in a single variable, perspectives and open problems

SummaryIn this paper theorems of P. Javor and N. Brillouët-J. Dhombres will be completed and a theorem of S. Wołodźko generalized, by describing complex-valued continuous solutions defined on a complex topological vector space of the Gołąb-Schinzel equation(*)