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Generalizations of Landau’s Inequality to Linear Operators

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Abstract

In 1913 Edmund Landau [13] proved that if f is continuous together with its first and second order derivatives in the interval [0, 1], if ‖ f ‖ = 1, ‖ f″‖=4, then

$$\left\| {f'} \right\| \mathbin{\lower.3ex\hbox{$\buildrel<\over {\smash{\scriptstyle=}\vphantom{_x}}$}} 4.$$
(1.1)

.

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References

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© 1972 Birkhäuser Verlag Basel

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Hille, E. (1972). Generalizations of Landau’s Inequality to Linear Operators. In: Butzer, P.L., Kahane, JP., Szökefalvi-Nagy, B. (eds) Linear Operators and Approximation / Lineare Operatoren und Approximation. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 20. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7283-6_1

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  • DOI: https://doi.org/10.1007/978-3-0348-7283-6_1

  • Publisher Name: Birkhäuser, Basel

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