Useful Inequalities (Jan 25 2023)

hbghlyj · 2023-7-22 12:30

Last edited by hbghlyj 2023-7-23 02:18 $type

G. H. Hardy, J. E. Littlewood, G. Pólya: Inequalities.
J. M. Steele: The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities.
D. S. Bernstein: Matrix Mathematics: Theory, Facts, and Formulas.
D. E. Knuth: The Art of Computer Programming (Volume 4)
A. W. Marshall, I. Olkin, B. C. Arnold: Inequalities: Theory of Majorization and Its Applications.
D. S. Mitrinovic: Analytic Inequalities.
D. S. Mitrinovic, J. E. Pecaric, A. M. Fink: Classical and New Inequalities in Analysis.
P. S. Bullen: A Dictionary of Inequalities.
P. S. Bullen: Handbook of Means and Their Inequalities.
J. Herman, R. Kucera, J. Simsa: Equations and Inequalities.
A. Lohwater: Introduction to Inequalities.
D. Dubhashi, A. Panconesi: Concentration of Measure for the Analysis of Randomized Algorithms.
S. Jukna: Extremal Combinatorics.
J. H. Spencer: Ten Lectures on the Probabilistic Method.
R. B. Ash: Information Theory.
Other sources:

Wikipedia: List of inequalities
Art of Problem Solving
Cut The Knot
functions.wolfram.com: Elementary Functions
Mathoverflow inequalities
F. Topsøe: Some bounds for the logarithmic function.
F. Topsøe: Bounds for entropy and divergence for distributions over a two-element set.
G. J. Woeginger: When Cauchy and Hölder Met Minkowski: A Tour through Well-Known Inequalities.
Zhi-Hong Sun: Inequalities for binomial coefficients.
Bounds on binomial coefficents
LaTeX template: cheat sheet

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[不等式] Useful Inequalities (Jan 25 2023)