Stability aspects of arithmetic functions

Stability aspects of arithmetic functions, II

“…A couple of results in that spirit was obtained by the author in [7] under some additional assumptions.…”

“…The present paper is a continuation of [7]. We deal with the stability problem for arithmetic additive and multiplicative functions in the sense of Hyers and Ulam (see [11]).…”

Orthogonalities and functional equations

“…Of course the condition that m and n are relatively prime, appearing in (3.16), causes that the direct method using Cauchy sequences cannot be used. Considering results of Erdős, Kátai, Máté (see [65,108,127]), Kochanek [109] proved the following. Then there exists c ∈ R such that |f (n) − c log n| ≤ ε for all n ∈ N.…”

“…Let P be the set of all prime numbers and for each n ∈ N let P n = {p ∈ P : p|n}. Some other stability results for additive arithmetic functions one can find in the papers [109][110][111] by Kochanek.…”

“…Ger [85] and Ger andŠemrl [88]). We cite here a result from Kochanek's paper [111] (one can see some other stability results in Kochanek's [109,110]; for the notations see Sect. 3.1.7 and [111]).…”