Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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GENERALIZED ISOMETRY IN NORMED SPACES

  • Received : 2020.11.28
  • Accepted : 2021.02.16
  • Published : 2022.01.31
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Abstract

Let g : X ⟶ Y and f : Y ⟶ Z be two maps between real normed linear spaces. Then f is called generalized isometry or g-isometry if for each x, y ∈ X, ║f(g(x)) - f(g(y))║ = ║g(x) - g(y)║. In this paper, under special hypotheses, we prove that each generalized isometry is affine. Some examples of generalized isometry are given as well.

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Acknowledgement

The author gratefully acknowledges the helpful comments of the anonymous referees.

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