On a generalization of the Cauchy functional equation. (Summary).
On the Baxter functional equation. (Summary).
On the Baxter functional equation.
Subgroups of the group Zn and a generalization of the Golab-Schinzel functional equation.
On a generalization of the Cauchy functional equation.
Subgroups of the Clifford group.
On the increasing solutions of the translation equation
Let M be a non-empty set endowed with a dense linear order without the smallest and greatest elements. Let (G,+) be a group which has a non-trivial uniquely divisible subgroup. There are given conditions under which every solution F: M×G → M of the translation equation is of the form for a ∈ M, x ∈ G with some non-trivial additive function c: G → ℝ and a strictly increasing function f: M → ℝ such that f(M) + c(G) ⊂ f(M). In particular, a problem of J. Tabor is solved.
The Christensen measurable solutions of a generalization of the Gołąb-Schinzel functional equation
Let K denote the set of all reals or complex numbers. Let X be a topological linear separable F-space over K. The following generalization of the result of C. G. Popa [16] is proved. Theorem. Let n be a positive integer. If a Christensen measurable function f: X → K satisfies the functional equation , then it is continuous or the set x ∈ X : f(x) ≠ 0 is a Christensen zero set.
On some iteration semigroups
Let be a disjoint iteration semigroup of diffeomorphisms mapping a real open interval onto . It is proved that if has a dense orbit possesing a subset of the second category with the Baire property, then for some diffeomorphism of onto the set of all reals . The paper generalizes some results of J.A.Baker and G.Blanton [3].
A note on stability of a linear functional equation of second order connected with the Fibonacci numbers and Lucas sequences.
Hyers-Ulam stability of the delay equation .
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