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Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 17, No. 2, pp. 107-112 (2001)
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Hyperstability of a class of linear functional equations

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Gyula Maksa and Zsolt Páles

Institute of Mathematics and Informatics, University of Debrecen, H-4010 Debrecen, Pf. 12, Hungary maksa@math.klte.hu, pales@math.klte.hu

**Abstract:** The aim of this note is to offer hyperstability results for linear functional equations of the form

f(s)+f(t)=\frac{1}{n}\sum_{i=1}^n f(s\phi_i(t)) \qquad (s,t\in S),

where $S$ is a semigroup and where $\phi_1,\dots,\phi_n\colon S\to S$ are pairwise distinct automorphisms of $S$ such that the set $\{\phi_1,\dots,\phi_n\}$ is a group equipped with the composition as the group operation. The main results state that if $f$ satisfies a stability inequality related to the above equation then it is also a solution of this equation.

**Keywords:** Hyperstability of functional equations, cocyle equation, generalized cocycle equation.

**Classification (MSC2000):** 39B72

**Full text of the article:**

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