AN INEQUALITY OF GRUSS LIKE VIA VARIANT OF POMPEIU'S MEAN VALUE THEOREM

The main of this paper is to establish an integral inequality of Gruss type by using a mean value theorem.

Keywords:

Pompeius mean value theorem Grss inequality, Hlders inequality,

PDF

___

[1] A. M. Acu, A. Babos and F. D. Sofonea, The mean value theorems and inequalities of Ostrowski type. Sci. Stud. Res. Ser. Math. Inform. 21 (2011), no. 1, 5-16.
[2] P. L. Cebysev, Sur less expressions approximatives des integrales de nies par les autres prises entre les memes limites, Proc. Math. Soc. Charkov, 2, 93-98, 1882.
[3] S.S. Dragomir, An inequality of Ostrowski type via Pompeiu's mean value theorem, J. of Inequal. in Pure and Appl. Math., 6(3) (2005), Art. 83.
[4] G. Gruss, Uber das maximum des absoluten Betrages von 1; Math. Z., 39, 215-226, 1935.
[5] I. Muntean, Extensions of some mean value theorems, Babes-Bolyai University, Faculty of Mathematics, Research Seminars on Mathematical Analysis, Preprint Nr. 7, 1991, 7-24.
[6] B. G. Pachpatte, On Gruss like integral inequalities via Pompeiu's mean value theorem, J. of Inequal. in Pure and Appl. Math. 6(1995), Article 82, 1{5.
[7] P.P Pecaric and S. Ungar, On an inequality of Gruss type, Mathematical Communications, 11(2006), 137-141.
[8] E. C. Popa, An inequality of Ostrowski type via a mean value theorem, General Mathematics Vol. 15, No. 1, 2007, 93-100.
[9] D. Pompeiu, Sur une proposition analogue au theoreme des accroissements nis, Mathematica (Cluj, Romania), 22 (1946), 143{146..
[10] F. Ahmad, N. A. Mir and M.Z. Sarikaya, An inequality of Ostrowski type via variant of Pompeiu's mean value theorem, J. Basic. Appl. Sci. Res., 4(4)204-211, 2014.
[11] M.Z. Sarikaya, and H. Budak, On an Inequality of Ostrowski Type via Variant of Pompeiu's Mean Value Theorem. Turkish Journal of Analysis and Number Theory, vol. 2, no. 3 (2014): 80-84.
[12] M.Z. Sarikaya, Some new integral inequalities via variant of Pompeiu's mean value theorem, RGMIA Research Report Collection, 17(2014), Article 6, 7 pp.