An application of an inequality of J. M. Aldaz
Keywords:
Inequalities, Young’s inequality, Cauchy-Schwarz inequality, Hölder’s inequality
Abstract
The aim of this paper is a to give a new proof that Hölder inequality is implied by the Cauchy-Schwarz inequality. Our proof is short and is based on the use of an inequality obtained by J. M. Aldaz in the paper: A stability version of Hölder’s inequality, Journal of Mathematical Analysis and Applications, 343, 2(2008), 842–852.
References
M. Akkouchi. Cauchy-Schwarz inequality implies Hölder’s inequality, RGMIA Res. Rep. Coll. 21 (2018), Art. 48, 3pp.
J. M. Aldaz. A stability version of Hölder’s inequality, Journal of Mathematical Analysis and Applications. 343(2) (2008), 842–852. doi:10.1016/j.jmaa.2008.01.104. Also available at the Mathematics ArXiv: arXiv:math.CA/0710.2307.
J. M. Aldaz. Self improvement of the inequality between arithmetic and geometric means. Journal of Mathematical Inequalities. 3 2(2009), 213–216.
C. Finol and M. Wojtowicz. Cauchy-Schwarz and Hölder’s inequalities are equivalent, Divulgaciones Matemáticas. 15 2(2007), 143–147.
C. A. Infantozzi. An introduction to relations among inequalities. Amer. Math. Soc. Meeting 700, Cleveland, Ohio 1972; Notices Amer. Math. Soc. 14 (1972), A819-A820, 121–122.
Yuan-Chuan Li and Sen-Yen Shaw. A proof of Hölder’s inequality using the Cauchy-Schwarz inequality. J. Inequal. Pure and Appl. Math., 7 2(2006), Art. 62.
A. W. Marshall and I. Olkin. Inequalities: Theory of Majorization and its Applications. Academic Press, New York-London, 1979.
D. S. Mtirinovic, J. E. Picaric and A. M. Fink. Classical and New Inequalities in Analysis. Kluwer Academic Publishers, 1993.
J. M. Aldaz. A stability version of Hölder’s inequality, Journal of Mathematical Analysis and Applications. 343(2) (2008), 842–852. doi:10.1016/j.jmaa.2008.01.104. Also available at the Mathematics ArXiv: arXiv:math.CA/0710.2307.
J. M. Aldaz. Self improvement of the inequality between arithmetic and geometric means. Journal of Mathematical Inequalities. 3 2(2009), 213–216.
C. Finol and M. Wojtowicz. Cauchy-Schwarz and Hölder’s inequalities are equivalent, Divulgaciones Matemáticas. 15 2(2007), 143–147.
C. A. Infantozzi. An introduction to relations among inequalities. Amer. Math. Soc. Meeting 700, Cleveland, Ohio 1972; Notices Amer. Math. Soc. 14 (1972), A819-A820, 121–122.
Yuan-Chuan Li and Sen-Yen Shaw. A proof of Hölder’s inequality using the Cauchy-Schwarz inequality. J. Inequal. Pure and Appl. Math., 7 2(2006), Art. 62.
A. W. Marshall and I. Olkin. Inequalities: Theory of Majorization and its Applications. Academic Press, New York-London, 1979.
D. S. Mtirinovic, J. E. Picaric and A. M. Fink. Classical and New Inequalities in Analysis. Kluwer Academic Publishers, 1993.
Published
2021-06-29
How to Cite
Akkouchi, M. (2021). An application of an inequality of J. M. Aldaz. Divulgaciones Matemáticas, 20(1), 91-94. Retrieved from https://produccioncientifica.luz.edu.ve/index.php/divulgaciones/article/view/36624
Section
Expository and historical papers
