Stability problem for number-theoretically multiplicative functions

Abstract

Abstract. We deal with the stability question for multiplicative mappings in the sense of number theory. It turns out that the conditional stability assumption:implies that f lies near to some number-theoretically multiplicative function. The domain of f can be general enough to admit, in special cases, the reduction of our result to the well known J. A. Baker -J. Lawrence -F. Zorzitto superstability theorem.

Stability aspects of arithmetic functions

“…This is a point of view different from that in [10] and may be regarded as more natural. An assumption of this type was proposed by R. Ger [4] for ordinary exponential mappings.…”

Richard's inequality, Cauchy-Schwarz's inequality and approximate solutions of Sincov's equation

“…Baker, J. Lawrence, F. Zorzitto [1], J.A. Baker [2], R. Ger, P. Šemrl [6], T. Kochanek, M. Lewicki [9], among others. However, taking into account the case of bounded solutions of (6) no full analogy can be observed, see Example 1.…”

Orthogonalities and functional equations

“…In the paper by Kochanek and Lewicki [113] the stability problem was formulated by means of a conditional inequality (cf. Baker et al [14], Baker [13])…”