{
  "id": "2210.06181",
  "version": "v1",
  "published": "2022-10-12T13:13:49.000Z",
  "updated": "2022-10-12T13:13:49.000Z",
  "title": "Five Trigonometric addition laws on semigroups",
  "authors": [
    "Aserrar Youssef",
    "Elqorachi Elhoucien"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "In this paper, we determine the complex-valued solutions of the following functional equations \\[g(x\\sigma (y)) = g(x)g(y)+f(x)f(y),\\quad x,y\\in S,\\]\\[f(x\\sigma (y)) = f(x)g(y)+f(y)g(x),\\quad x,y\\in S,\\]\\[f(x\\sigma (y)) = f(x)g(y)+f(y)g(x)-g(x)g(y),\\quad x,y\\in S,\\]\\[f(x\\sigma(y))=f(x)g(y)+f(y)g(x)+\\alpha g(x\\sigma(y)),\\quad x,y\\in S,\\]\\[f(x\\sigma(y))=f(x)g(y)-f(y)g(x)+\\alpha g(x\\sigma(y)),\\quad x,y\\in S,\\] where $S$ is a semigroup, $\\alpha \\in \\mathbb{C}\\backslash \\lbrace 0\\rbrace$ is a fixed constant and $\\sigma :S\\rightarrow S$ an involutive automorphism.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-12T13:13:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "39B32",
      "39B52"
    ],
    "keywords": [
      "trigonometric addition laws",
      "functional equations",
      "complex-valued solutions",
      "fixed constant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}