Generalizations of Cauchy-Schwarz inequality in unitary spaces. (English) Zbl 1372.26021

Tuo, Leng

J. Inequal. Appl. 2015, Paper No. 201, 6 p. (2015).

Summary: In this paper, we give a generalization of Cauchy-Schwarz inequality in unitary spaces and obtain its integral analogs. As an application, we establish an inequality for covariances.

MSC:

26D15	Inequalities for sums, series and integrals
62J10	Analysis of variance and covariance (ANOVA)

Keywords:

Cauchy-Schwarz inequality; unitary space; positive measure

References:

[1]	Dragomir, SS, A survey on the Cauchy-buniakowsky-Schwarz type discrete inequalities, J. Inequal. Pure Appl. Math., 4, (2003)
[2]	Ackermann, N, A Cauchy-Schwarz type inequality for bilinear integrals on positive measures, Proc. Am. Math. Soc., 133, 2647-2656, (2005) · Zbl 1066.26013
[3]	Alzer, H, A refinement of the Cauchy-Schwarz inequality, J. Math. Anal. Appl., 168, 596-604, (1992) · Zbl 0763.26012
[4]	Alzer, H, On the Cauchy-Schwarz inequality, J. Math. Anal. Appl., 234, 6-14, (1999) · Zbl 0933.26010
[5]	Carbery, A, A multilinear generalization of the Cauchy-Schwarz inequality, Proc. Am. Math. Soc., 132, 3141-3152, (2004) · Zbl 1043.05011
[6]	Dragomir, SS, On the Cauchy-buniakowsky-Schwarz inequality for sequences in inner product space, Math. Inequal. Appl., 3, 385-398, (2000) · Zbl 0964.26013
[7]	Masjed-Jamei, M, A functional generalization of the Cauchy-Schwarz inequality and some subclasses, Appl. Math. Lett., 22, 1335-1339, (2009) · Zbl 1173.26323
[8]	Mitrinović, DS, Pećarić, JE, Fink, AM: Classical and New Inequalities in Analysis. Kluwer Academic, Dordrecht (1993) · Zbl 0771.26009
[9]	Wada, S, On some refinement of the Cauchy-Schwarz inequality, Linear Algebra Appl., 420, 433-440, (2007) · Zbl 1121.47010
[10]	Rudin, W: Real and Complex Analysis. McGraw-Hill, New York (1987) · Zbl 0925.00005
[11]	Fisher, RA: Statistical Methods, Experimental Design, and Scientific Inference. Oxford University Press, New York (1990) · Zbl 0705.62003