{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "VPBSH2KDFD"
    }
  ],
  "body": "\n## Summary\n\nThe Pexider equation is the [[functional equation|SRAN4EKWS0]] $f(x + y) = g(x) + h(y)$ with three unknown functions $f, g, h \\colon \\R \\to \\R$.\nIt generalizes Cauchy's additive equation, which is the case $f = g = h$.\nIts solutions are $f = A + a + b$, $g = A + a$ and $h = A + b$, where $A$ is an [[additive function|KF719SZD5T]] and $a, b$ are constants.\nEquations of this kind, with several unknown functions in the place of one, are called Pexiderized forms of the classical equations.\n\n## Explanations\n\n### L1 human\n\nThe equation asks for three functions that fit together: the first one at a sum is the second at one term plus the third at the other.\nAllowing three different functions gives only a little more freedom than Cauchy's equation.\nFor example, $f(x) = x + 3$, $g(x) = x + 1$ and $h(x) = x + 2$ solve it.\nEvery solution differs from an additive function only by constant shifts.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "39B22",
      "39B52"
    ],
    "name": "Pexider equation",
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Functional_equation"
      }
    ],
    "specializes": [
      "SRAN4EKWS0"
    ],
    "tag": "CTMRG74JN0"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/CTMRG74JN0/",
  "links": [
    {
      "field": "specializes",
      "target": "SRAN4EKWS0"
    }
  ],
  "markdown": "https://tamnd.github.io/math2/node/CTMRG74JN0.md",
  "msc": [
    "39B22",
    "39B52"
  ],
  "name": "Pexider equation",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/CTM/CTMRG74JN0.md",
  "status": null,
  "tag": "CTMRG74JN0",
  "uri": "m2://CTMRG74JN0",
  "url": "https://tamnd.github.io/math2/wiki/pexider-equation/",
  "writing": {
    "tag": "CTMRG74JN0",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      },
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}