在本文中，我們建立了新的Čebyšev-Grüss型不等式靠著使用在Montgomery等式的Pecaric的延伸。

In the present note we establish new Čebyšev-Grüss type inequalities by using Pecaric’s extension of the Montgomery identity.

中文目錄
１前言………………………………………………… P1.
　定理１.１……………………………………………P1.
　定理１.２……………………………………………P2.
２主要結果…………………………………………… P2.
　定理２.１……………………………………………P3.
　定理２.２……………………………………………P6.
　定理２.３……………………………………………P7.
　定理２.４……………………………………………P8.
３參考文獻…………………………………………… P10.
  
  英文目錄
１Introduction……………………………………… P11.
　Theorem1.1………………………………………….P11.
　Theorem1.2………………………………………….P12.
２Main results……….………………………………P12.
　Theorem2.1………………………………………….P14.
　Theorem2.2………………………………………….P16.
　Theorem2.3………………………………………….P17.
　Theorem2.4………………………………………….P19.
３References………………………………………… P20.

[1] P.L. Cebysev Sue les expressions approximatives des integrals definies par les autres prises entre les memes limites, Proc. Math. Soc. Charkov, 2 (1882), 93-98.
[2] G. GRUSS, Uber das maximum des absoluten Betrages von [1/(b-a)]∫_a¯b f(x)g(x)dx-[1/(b-a)^2]∫_a¯b f(x)dx∫_a¯b g(x)dx, Math. Z., 39 (1935), 215-226.
[3] D.S. MITRINOVIC, J.E. PECARIC AND A.M. FINK, Inequalities Involving Functions and Their Integrals and Derivatives, Kluwer Academic Publishers, Dordrecht, 1991.
[4] D.S. MITRINOVIC, J.E. PECARIC AND A.M. FINK, Classical and New Inequalities in Analysis, Kluwer Academic Publishers, Dordrecht, 1993.
[5] B.G. PACHPATTE. New weighted multivariate Gruss type inequalities, J. Inequal. Pure and Appl. Math., 4(5), Art. 108. 1-9, 2003.  [ONLINE:http://jipam.vu.edu.au/article.php?sid=349].
[6] B.G. PACHPATTE. On Cebysev-Gruss type inequalities via pecaric's extension of the Montgomery identity, J. Inequal. Pure and Appl. Math 7(1) Art11, 1-4. (2006).
[7] J.E. PECARIC, On the Cebysev inequality, Bul. Sti. Tehn. Inst. Politehn.
 〞Train Vuia〞 Timisora, 25(39) (1) (1980), 5-9.