Search Results

Journal: Annales Mathematicae Silesianae

A Kannappan-cosine functional equation on semigroups

Ahmed Jafar , Omar Ajebbar , Elhoucien Elqorachi

Language: EN | Published: 27-04-2024 | Abstract | pp. 143-154

In this paper we determine the complex-valued solutions of the Kannappan-cosine functional equation g(xyz₀) = g(x)g(y) − f(x)f(y), x,y∈S, where S is a semigroup and z₀ is a fixed element in S.

2024-04-27



Journal: Annales Mathematicae Silesianae

n-th root selections in fields

Paweł Gładki

Language: EN | Published: 22-06-2019 | Abstract | pp. 106-120

In this work we generalize the results of [9] to the higher level case: we define n-th root selections in fields of characteristic ≠2, that is subgroups of the multiplicative group of a field whose existence is equivalent to the existence of a partial inverse of the x↦xⁿ function, provide necessary and sufficient conditions for such a subgroup to exist, study their existence under field extensions, and give some structural results describing the behaviour of maximal n-th root selection fields.

2019-06-22



Journal: Annales Mathematicae Silesianae

A variant of d'Alembert's functional equation on semigroups with endomorphisms

Ahmed Akkaoui , Mohamed El Fatini , Brahim Fadli

Language: EN | Published: 22-03-2022 | Abstract | pp. 1-14

Let S be a semigroup, and let ϕ,ψ:S→S be two endomorphisms (which are not necessarily involutive). Our main goal in this paper is to solve the following generalized variant of d’Alembert’s functional equation
f(xϕ(y))+f(ψ(y)x) = 2f(x)f(y), x,y∈S,
where f:S→ℂ is the unknown function by expressing its solutions in terms of multiplicative functions. Some consequences of this result are presented.

2022-03-22