Goła̧b–Schinzel equation on cylinders

Abstract

We determine continuous solutions of the Go lab-Schinzel functional equation on cylinders.

From invariance under binomial thinning to unification of the Cauchy and the Gołąb-Schinzel-type equations

“…For more recent contributions on the Goł ąb-Schinzel equation and its generalizations consult e.g. [7], [8], [9], [4] and [11]. In particular, the latter paper reveals yet another probabilistic (stable laws and random walks) connection of the Goł ąb-Schinzel equation, treated there as a disguised form of the Goldie equation.…”

From Invariance Under Binomial Thinning to Unification of the Cauchy and the Gołąb–Schinzel-Type Equations

“…For more recent contributions on the Go lab-Schinzel equation and its generalizations consult e.g. [4,[7][8][9] and [11]. In particular, the latter paper reveals yet another probabilistic (stable laws and random walks) connection of the Go lab-Schinzel equation, treated there as a disguised form of the Goldie equation.…”

“…s 0 = 0: Then (11) together with (8) imply that a = 0. Consequently, f is as given in (9). By ( 13) we have h(s) = 0 for s > 0.…”