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109.26 A simple self-improvement of the Cauchy-Schwarz inequality

Published online by Cambridge University Press:  20 June 2025

Reza Farhadian
Affiliation:
Department of Statistics, Razi University, Kermanshah, Iran e-mail: farhadian.reza@yahoo.com
Vadim Ponomarenko
Affiliation:
Department of Mathematics and Statistics, San Diego State University, San Diego, CA, USA e-mail: vponomarenko@sdsu.edu

Abstract

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Copyright
© The Authors, 2025 Published by Cambridge University Press on behalf of The Mathematical Association

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References

Cauchy, A.-L., Sur les formules qui resultent de l’emploie du signe et sur > ou <, et sur les moyennes entre plusieurs quantites, Cours d’Analyse, 1er Partie: Analyse Algebrique, (1821), pp. 373377.Google Scholar
Bunyakovsky, V. Y., Sur quelques inegalites concernant les integrales ordinaires et les integrales aux differences finies, Mem. Acad. St. Petersburg (Ser. 7) 1 (1859), pp. 118.Google Scholar
Schwarz, H. A., Über ein die Flächen kleinsten Flächeninhalts betreffendes Problem der Variationsrechnung, Acta Soc. Scient. Fen. 15 (1885), pp. 315362.Google Scholar
Callebaut, D. K., Generalization of the Cauchy-Schwarz inequality, J. Math. Anal. Appl. 12 (1965), pp. 491494.CrossRefGoogle Scholar
Chee-Eng Ng, D., Another proof of the Cauchy-Schwarz inequality with complex algebra, Math. Gaz. 93 (March 2009) pp. 104105CrossRefGoogle Scholar
Dragomir, S. S., A survey on Cauchy-Bunyakovsky-Schwarz type discrete inequalities, J. Inequal. Pure Appl. Math. 4 (2003), Art. 63.Google Scholar
Farhadian, R., Remark on Cauchy-Schwarz inequality, Math. Gaz. 107CrossRefGoogle Scholar
Lord, N. J., Cauchy-Schwarz via collisions, Math. Gaz. 99 (November 2015) pp. 541542.CrossRefGoogle Scholar
Masjed-Jamei, M., Dragomir, S. S., Srivastava, H. M. , Some generalizations of the Cauchy-Schwarz and the Cauchy-Bunyakovsky inequalities involving four free parameters and their applications, Mathematical and Computer Modelling, 49 (2009), pp. 19601968. CrossRefGoogle Scholar
Yin, S., A new generalization on Cauchy-Schwarz inequality, Journal of Function Spaces, (2017), Art. ID 9576375.Google Scholar
Walker, S. G., A self-improvement to the Cauchy-Schwarz inequality, Statistics & Probability Letters. 122 (2017), pp. 8689.CrossRefGoogle Scholar