Über eine Lösungsmethode gewisser Funktionalgleichungen

Difference operators, distributions and functional equations

“…The functional equation (8), considered in this final section, was discussed in a similar spirit in [2] in the case n -2. Similar equations have been studied in [6], [11], [12], [18], [22], [23] and [27].…”

Problems in the regularity theory of functional equations

“…To conclude this section, we mention that beside the regularity improving theorems, there is another approach to solving functional equations with weak regularity assumptions discovered by Fenyő [Feny56]. The idea is to consider "locally integrable solutions" as distributions.…”

Distributional Solutions of Wilson's Functional Equations With Involution and Their Erdös' Problem

“…3) are generalizations of d'Alembert's functional equation. Among others Wilson's functional equation was studied by Wilson [31,32], Kaczmarz [24], van der Lyn [29], Fenyö [19], Angheluta [3], Aczél Chung, and Ng [2], Chung, Ebanks, Ng and Sahoo [10], Aczél [1] and Stetkaer in [28]. Recently, Chung and Sahoo [8] solve the equation (1.2) and (1.3) for arbitrary commutative semigroup.…”