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A companion of the Grüss inequality and applications. (English) Zbl 1057.26015

Summary: A companion of the Grüss inequality in the general setting of measurable spaces and abstract Lebesgue integrals is proven. Some particular inequalities are mentioned as well. An application for the moments of the guessing mapping is also provided.

MSC:

26D15 Inequalities for sums, series and integrals
28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
94A15 Information theory (general)
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References:

[1] Andrica, D.; Badea, C., Grüss’ inequality for positive linear functionals, Periodica Math. Hungarica, 19, 2, 155-167 (1988) · Zbl 0619.26011
[2] Dragomir, S. S., A generalization of Grüss’s inequality in inner product spaces and applications, J. Math. Anal. Appl., 237, 1, 74-82 (1999) · Zbl 0943.46011
[3] Dragomir, S. S., Integral Grüss inequality for mappings with values in Hilbert spaces and applications, J. Korean Math. Soc., 38, 6, 1261-1273 (2001) · Zbl 1016.26015
[4] Cerone, P.; Dragomir, S. S., A refinement of Grüss’ inequality and applications, RGMIA Res. Rep. Coll., 5, 2 (2002), Article 14 · Zbl 1143.26009
[5] Fink, A. M., A treatise on Grüss’ inequality. Analytic and geometric inequalities and applications, Math. Appl., 478, 93-113 (1999) · Zbl 0982.26012
[6] Pec̆aric, J., On some inequalities analogous to Grüss inequality, Mat. Vesnik, 4, 17, 197-202 (1980) · Zbl 0469.26008
[7] Massey, J. L., Guessing and entropy, (Proc. 1994 IEEE Int. Symp. on Inf. Th.. Proc. 1994 IEEE Int. Symp. on Inf. Th., Trondheim, Norway, 1994 (1994)), 204
[8] Arikan, E., An inequality on guessing and its application to sequential decoding, IEEE Tran. Inf. Th., 42, 1, 99-105 (1996) · Zbl 0845.94020
[9] Boztaş, S., Comments on “An inequality of guessing and its applications to sequential decoding”, IEEE Tran. Inf. Th., 43, 6, 2062-2063 (1997) · Zbl 1053.94536
[10] Dragomir, S. S.; Boztaş, S., Some estimates of the average number of guesses to determine a random variable, (Proc. 1997 IEEE Int. Symp. on Inf. Th.. Proc. 1997 IEEE Int. Symp. on Inf. Th., Ulm, Germany, 1997 (1997)), 159
[11] Dragomir, S. S.; Boztas, S., Estimation of arithmetic means and their applications in guessing theory, Mathl. Comput. Modelling, 28, 10, 31-43 (1998) · Zbl 0992.94022
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