Dragomir, S. S. A companion of the Grüss inequality and applications. (English) Zbl 1057.26015 Appl. Math. Lett. 17, No. 4, 429-435 (2004). 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. Cited in 4 Documents MSC: 26D15 Inequalities for sums, series and integrals 28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence 94A15 Information theory (general) Keywords:Grüss inequality; Lebesgue integral; guessing mapping PDFBibTeX XMLCite \textit{S. S. Dragomir}, Appl. Math. Lett. 17, No. 4, 429--435 (2004; Zbl 1057.26015) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.