Orthogonally additive functions modulo a discrete subgroup

Measurable orthogonally additive functions modulo a discrete subgroup

“…Now we are prepared to proceed to our main result. The technical assumptions appearing below have been already considered (see [7], [3], [6] and [14]). In the last section we present a counterexample showing that condition (G2) is essential.…”

“…According to [14,Lemma 4] there exist a continuous additive function a : G → H and a continuous at zero quadratic function q : G → H such that (…”

Orthogonalities and functional equations

“…). The last result was generalized first by Brzdęk [32] (with the domain being an orthogonality space and with the assumption of continuity at the origin) and then by Wyrobek [198] who was working in an Abelian topological group in the domain with the assumption of continuity at an arbitrary point.…”

“…In [33], Brzdęk studied universally, Christensen or Baire measurable functions defined on a real linear topological space with axiomatic orthogonality relation by Rätz, and with values in C. In [198] …”

“…Studying pexiderized forms of the Cauchy difference often brings interesting and surprising results (cf., e.g., Sikorska [170]). Pexiderized forms of (3.13) were investigated by Bajger [12] and Wyrobek-Kochanek [199].…”