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Improvement of some inequalities of Euler-Grüss type. (English) Zbl 1083.26016
The key result of this paper is a Grüss type inequality which improves Lemma 1 from [{\it Lj. Dedić, M. Matić} and {\it J. Pečarić}, Comput. Math. Appl. 41, No. 7-8, 843--856 (2001; Zbl 0984.26011)]. The author applies this key result in order to improve all the Euler-Grüss type inequalities from the above mentioned paper. All the improved inequalities are sharp.

MSC:
26D15Inequalities for sums, series and integrals of real functions
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Full Text: DOI
References:
[1] Matić, M.; Pečaxić, J.; Ujević, N.: Improvement and further generalization of some inequalities of ostrowskigrüss type. Computers math. Applic. 39, No. 3/4, 161-175 (2000) · Zbl 0952.26013
[2] Cheng, X. -L.: Improvement of some Ostrowski-grüss type inequalities. Computers math. Applic. 42, No. 1/2, 109-114 (2001) · Zbl 0980.26011
[3] Pearce, C. E. M.; Pečaríc, J.; Ujevic, N.; Varošanec, S.: Generalizations of some inequalities of Ostrowski-grüss type. Math. inequal. Appl. 3, No. 1, 25-34 (2000) · Zbl 0978.26011
[4] Dedić, Lj.; Matić, M.; Pečarić, J.: Some inequalities of Euler-grüss type. Computers math. Applic. 41, No. 7/8, 843-856 (2001) · Zbl 0984.26011
[5] Krylov, V. I.: Approximate calculation of integrals. (1962) · Zbl 0111.31801
[6] Dedić, Lj.; Matić, M.; Pečarić, J.: On generalizations of Ostrowski inequality via some Euler-type identities. Math. inequal. Appl. 3, No. 3, 337-353 (2000) · Zbl 0965.26014
[7] Abramowitz, M.; Stegun, I. A.: Handbook of mathematical functions with formulae, graphs and mathematical tables. (1965) · Zbl 0171.38503