Saejung, S.; Senasukh, J. On stability and hyperstability of additive equations on a commutative semigroup. (English) Zbl 1438.39051 Acta Math. Hung. 159, No. 2, 358-373 (2019). The main aim of this paper is to prove the stability and hyperstability of additive functional equations on restricted domains (i.e., on subsets of a commutative semigroup). The majority of the proofs is based on the modified version of a fixed point theorem due to J. Brzdȩk [Fixed Point Theory Appl. 2013, Paper No. 285, 9 p. (2013; Zbl 1297.39026)]. The authors introduce the concepts of modulus-additive and approximately modulus-additive functions and deduce some stability and hyperstability results for the modulus-additive equation. They also obtain some results for the radical quadratic functional equation. Reviewer: Eszter Gselmann (Debrecen) Cited in 3 Documents MSC: 39B82 Stability, separation, extension, and related topics for functional equations 47H10 Fixed-point theorems Keywords:hyperstability; stability; modulus-additive function; radical quadratic function Citations:Zbl 1297.39026 PDFBibTeX XMLCite \textit{S. Saejung} and \textit{J. Senasukh}, Acta Math. Hung. 159, No. 2, 358--373 (2019; Zbl 1438.39051) Full Text: DOI