Continuous Solutions of Conditional Composite Type Functional Equations

Abstract

Abstract. It is known that some problems in meteorology and fluid dynamics lead to Go lab-Schinzel type equations on a restricted domain. Inspired by a question of Professor L. Reich we determine the solutions of conditional composite type functional equations related to the Go lab-Schinzel equation.Mathematics Subject Classification (2010). 39B12, 39B22.

Positive Homogeneity of the Principle of Equivalent Utility

“…Since f and F are continuous, f is strictly increasing and f (x) > 0 for x ∈ R, applying Theorem 3.4 in Ref. [6], we conclude that one of the following two possibilities holds:…”

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.…”

Functional equations of the Goła̧b-Schinzel type on a cone

“…Further going pexiderization of the Gołab-Schinzel equation have been investigated in [5]- [6] and [10]- [11]. In a recent paper [8] the results of [1] and [19] have been generalized. More precisely, the continuous solutions of the equations f (x + g(x)y) = f (x) f (y) whenever x, y, x + g(x)y ≥ 0 ( 4 ) and f (x + g(x)y) = f (x) f (y) for x, y ∈ [0, ∞)…”

“…In the present paper, applying the results of [8], we deal with a similar problem, but in a much more general setting. Namely, given a real linear space X and a convex cone C in X , that is a nonempty subset of X such that αx + βy ∈ C for x, y ∈ C and α, β ∈ [0, ∞), we determine the solutions of the equation…”