Functional equations of the Goła̧b-Schinzel type on a cone

Abstract

We determine the solutions of conditional composite type functional equations related to some problems in mathematical meteorology and fluid mechanics.

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.…”

Goła̧b–Schinzel equation on cylinders

“…Therefore, as F (0) = 0, taking ( 14) into account, we obtain (8). Note also that, making use of ( 13) and ( 14), we get…”

“…All of them concern the case where an unknown function f is a real function of a real variable. In a recent paper [8] equation (1) has been investigated in a more general setting, namely on a convex cone in a real linear space.…”