Geodesic
Chebyshev--Gr\"uss-type inequalities via discrete oscillations
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2014), pp. 63-89

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The classical form of Grüss' inequality, first published by G. Grüss in 1935, gives an estimate of the difference between the integral of the product and the product of the integrals of two functions. In the subsequent years, many variants of this inequality appeared in the literature. The aim of this paper is to introduce a new approach, presenting a new Chebyshev–Grüss-type inequality and applying to different well-known linear, not necessarily positive, operators. Some conjectures are presented. We also compare the new inequalities with some older results. In some cases this new approach gives better estimates than the ones already known. 
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     title = {Chebyshev--Gr\"uss-type inequalities via discrete oscillations},
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Heiner Gonska; Ioan Raşa; Maria-Daniela Rusu. Chebyshev--Gr\"uss-type inequalities via discrete oscillations. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2014), pp. 63-89. http://geodesic.mathdoc.fr/item/BASM_2014_1_a4/