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The maximum of a quasismooth function


Authors: J. Ernest Wilkins and Theodore R. Hatcher
Journal: Math. Comp. 41 (1983), 573-589
MSC: Primary 26D20
DOI: https://doi.org/10.1090/S0025-5718-1983-0717704-1
MathSciNet review: 717704
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Abstract: Let Z be the class of real-valued functions, defined and continuous on the closed interval $ I = [ - 1,1]$, such that $ f( \pm 1) = 0$ and $ \vert f(\xi ) - 2f\{ (\xi + \eta )/2\} + f(\eta )\vert \leqslant \vert\xi - \eta \vert$ for all $ \xi $ and $ \eta $ in I. Let $ K = {\sup _{f \in Z}}{\max _{x \in I}}\vert f(x)\vert$. We will prove that $ 13/10 \leqslant K \leqslant 1014/779 < 1.301669$.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1983-0717704-1
Article copyright: © Copyright 1983 American Mathematical Society