Jensen’s functional equation on semigroups

Akkaoui, Ahmed

doi:10.1007/s10474-023-01341-7

Acta Math. Hungar.

2023

DOI: 10.1007/s10474-023-01341-7

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Jensen’s functional equation on semigroups

Ahmed Akkaoui

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2024

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New Results About Quadratic Functional Equation on Semigroups

Akkaoui,

Fadli

2024

Annales Mathematicae Silesianae

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Let S be a semigroup, let (H, +) be a uniquely 2-divisible, abelian group and let φ, ψ be two endomorphisms of S that need not be involutive. In this paper, we express the solutions f : S → H of the following quadratic functional equation f ( x ϕ ( y ) ) + f ( ψ ( y ) x ) = 2 f ( x ) + 2 f ( y ) , x , y ∈ S , f\left( {x\varphi \left( y \right)} \right) + f\left( {\psi \left( y \right)x} \right) = 2f\left( x \right) + 2f\left( y \right),\,\,\,\,\,x,y \in S, in terms of bi-additive maps and solutions of the symmetrized additive Cauchy equation. Some applications of this result are presented.

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New Results About Quadratic Functional Equation on Semigroups

Akkaoui,

Fadli

2024

Annales Mathematicae Silesianae

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Jensen’s functional equation on semigroups

Cited by 1 publication

References 13 publications

New Results About Quadratic Functional Equation on Semigroups

New Results About Quadratic Functional Equation on Semigroups

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