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2 results

  • A New Proof of the Snake Theorem

  • Lee L. Keener
  • Journal:
    Canadian Mathematical Bulletin / Volume 25 / Issue 2 / 01 June 1982
    Published online by Cambridge University Press:
    20 November 2018, pp. 234-237
    Print publication:
    01 June 1982
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  • The Snake Theorem (terminology of Krein), due to Karlin in its original form, has been periodically improved. The theorem shows under appropriate conditions the existence of a function p* from a Tchebycheff space T, with a graph that alternately "touches" the graphs of functions f and g where f < g and f ≤ p* ≤ g on a compact interval [a, b]. The number of "touchings" depends upon the dimension of T. In this paper the conditions assumed are not the weakest known (see Gopinath and Kurshan, J. of Approximation Theory 21 (1977), 151–173), but the apparently new proof offered is elementary and fairly short. f and g are not assumed continuous.