Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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SOLUTIONS AND STABILITY OF TRIGONOMETRIC FUNCTIONAL EQUATIONS ON AN AMENABLE GROUP WITH AN INVOLUTIVE AUTOMORPHISM

  • Received : 2017.12.21
  • Accepted : 2018.02.06
  • Published : 2019.01.31
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Abstract

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.

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References

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