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오늘 본 자료
VARIANTS OF WILSON'S FUNCTIONAL EQUATION ON SEMIGROUPS
Ajebbar, Omar,Elqorachi, Elhoucien Korean Mathematical Society 2020 대한수학회논문집 Vol.35 No.3
Given a semigroup S generated by its squares equipped with an involutive automorphism 𝝈 and a multiplicative function 𝜇 : S → ℂ such that 𝜇(x𝜎(x)) = 1 for all x ∈ S, we determine the complex-valued solutions of the following functional equations f(xy) + 𝜇(y)f(𝜎(y)x) = 2f(x)g(y), x, y ∈ S and f(xy) + 𝜇(y)f(𝜎(y)x) = 2f(y)g(x), x, y ∈ S.
Ajebbar, Omar,Elqorachi, Elhoucien Korean Mathematical Society 2019 대한수학회논문집 Vol.34 No.1
Given ${\sigma}:G{\rightarrow}G$ an involutive automorphism of a semigroup G, we study the solutions and stability of the following functional equations $$f(x{\sigma}(y))=f(x)g(y)+g(x)f(y),\;x,y{\in}G,\\f(x{\sigma}(y))=f(x)f(y)-g(x)g(y),\;x,y{\in}G$$ and $$f(x{\sigma}(y))=f(x)g(y)-g(x)f(y),\;x,y{\in}G$$, from the theory of trigonometric functional equations. (1) We determine the solutions when G is a semigroup generated by its squares. (2) We obtain the stability results for these equations, when G is an amenable group.
THE STABILITY OF A COSINE-SINE FUNCTIONAL EQUATION ON ABELIAN GROUPS
Omar Ajebbar,Elhoucien Elqorachi,Rassias Themistocles M. 경남대학교 수학교육과 2019 Nonlinear Functional Analysis and Applications Vol.24 No.3
In this paper we establish the stability of the functional equation \begin{equation*}f(x-y)=f(x)g(y)+g(x)f(y)+h(x)h(y),\;\; x,y \in G, \end{equation*}where $G$ is an abelian group.