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The Type of Minimal Branching Geodesics Defines the Norm in a Normed Space

Abstract

In this paper, we investigate the inverse problem to the minimal branching geodesic searching problem in a normed space. Let us consider a normed space. Then the form of the minimal branching geodesic is determined. We must find all possible normed spaces with the same form of the minimal branching geodesics as the one in the considered normed space. The case of Euclidean norms is analyzed in detail.

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References

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Correspondence to I. L. Laut.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 2, pp. 67–77, 2013.

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Laut, I.L., Ovsyannikov, Z.N. The Type of Minimal Branching Geodesics Defines the Norm in a Normed Space. J Math Sci 203, 799–805 (2014). https://doi.org/10.1007/s10958-014-2169-4

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Keywords

  • Banach Space
  • Unit Circle
  • Normed Space
  • Euclidean Norm
  • Relative Interior