### Abstract

The aim of this note is to offer hyperstability results for linear functional equations of the form f(s) + f(t) = 1/n ∑_{i=1} ^{n} f(sψ_{i}(t)) (s, t ∈ S), where S is a semigroup and where ψ_{1}, . . . , ψ_{n}: S → S are pairwise distinct automorphisms of S such that the set {ψ_{1}, . . . , ψ_{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.

Original language | English |
---|---|

Pages (from-to) | 107-112 |

Number of pages | 6 |

Journal | Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis |

Volume | 17 |

Issue number | 2 |

Publication status | Published - 2001 |

### Fingerprint

### Keywords

- Cocyle equation
- Generalized cocycle equation
- Hyperstability of functional equations

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis*,

*17*(2), 107-112.

**Hyperstability of a class of linear functional equations.** / Maksa, Gyula; Páles, Z.

Research output: Contribution to journal › Article

*Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis*, vol. 17, no. 2, pp. 107-112.

}

TY - JOUR

T1 - Hyperstability of a class of linear functional equations

AU - Maksa, Gyula

AU - Páles, Z.

PY - 2001

Y1 - 2001

N2 - The aim of this note is to offer hyperstability results for linear functional equations of the form f(s) + f(t) = 1/n ∑i=1 n f(sψi(t)) (s, t ∈ S), where S is a semigroup and where ψ1, . . . , ψn: S → S are pairwise distinct automorphisms of S such that the set {ψ1, . . . , ψn} 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.

AB - The aim of this note is to offer hyperstability results for linear functional equations of the form f(s) + f(t) = 1/n ∑i=1 n f(sψi(t)) (s, t ∈ S), where S is a semigroup and where ψ1, . . . , ψn: S → S are pairwise distinct automorphisms of S such that the set {ψ1, . . . , ψn} 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.

KW - Cocyle equation

KW - Generalized cocycle equation

KW - Hyperstability of functional equations

UR - http://www.scopus.com/inward/record.url?scp=1342340240&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1342340240&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:1342340240

VL - 17

SP - 107

EP - 112

JO - Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis

JF - Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis

SN - 1786-0091

IS - 2

ER -