• Journal of the Chungcheong Mathematical Society
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• v.9 no.1
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• pp.123-128
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• 1996

This paper is to study the regular $^*$ semigroup, to define the self-involutive semi-group, to introduce the properties of the self-involutive semigroup, and to generalize the maximum idempotent-separating congruence which was found by conditioning self-involutive semigroups.

• Bulletin of the Korean Mathematical Society
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• v.33 no.2
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• pp.213-219
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• 1996

In this note we study the representations on Hilbert space of involutive semigroups, i.e., semigroups endowed with an involutive antiautomorphism. This subject is studied by K. H. Neeb, and some interesting results are ivestigated ([3]).

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.55-82
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• 2019

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.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.711-722
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• 2020

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.