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On stability and hyperstability of additive equations on a commutative semigroup. (English) Zbl 1438.39051

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.

MSC:

39B82 Stability, separation, extension, and related topics for functional equations
47H10 Fixed-point theorems

Citations:

Zbl 1297.39026
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