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

Year 2015, Volume: 3 Issue: 1, 29 - 35, 01.04.2015

Mehmet Zeki Sarıkaya , Hüseyin Budak

Abstract

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

References

  • [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.

Year 2015, Volume: 3 Issue: 1, 29 - 35, 01.04.2015

Mehmet Zeki Sarıkaya , Hüseyin Budak

Abstract

References

  • [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.
There are 12 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Mehmet Zeki Sarıkaya

Hüseyin Budak

Publication Date April 1, 2015
Submission Date July 10, 2014
Published in Issue Year 2015 Volume: 3 Issue: 1

Cite

APA Sarıkaya, M. Z., & Budak, H. (2015). AN INEQUALITY OF GRUSS LIKE VIA VARIANT OF POMPEIU’S MEAN VALUE THEOREM. Konuralp Journal of Mathematics, 3(1), 29-35.
AMA Sarıkaya MZ, Budak H. AN INEQUALITY OF GRUSS LIKE VIA VARIANT OF POMPEIU’S MEAN VALUE THEOREM. Konuralp J. Math. April 2015;3(1):29-35.
Chicago Sarıkaya, Mehmet Zeki, and Hüseyin Budak. “AN INEQUALITY OF GRUSS LIKE VIA VARIANT OF POMPEIU’S MEAN VALUE THEOREM”. Konuralp Journal of Mathematics 3, no. 1 (April 2015): 29-35.
EndNote Sarıkaya MZ, Budak H (April 1, 2015) AN INEQUALITY OF GRUSS LIKE VIA VARIANT OF POMPEIU’S MEAN VALUE THEOREM. Konuralp Journal of Mathematics 3 1 29–35.
IEEE M. Z. Sarıkaya and H. Budak, “AN INEQUALITY OF GRUSS LIKE VIA VARIANT OF POMPEIU’S MEAN VALUE THEOREM”, Konuralp J. Math., vol. 3, no. 1, pp. 29–35, 2015.
ISNAD Sarıkaya, Mehmet Zeki - Budak, Hüseyin. “AN INEQUALITY OF GRUSS LIKE VIA VARIANT OF POMPEIU’S MEAN VALUE THEOREM”. Konuralp Journal of Mathematics 3/1 (April 2015), 29-35.
JAMA Sarıkaya MZ, Budak H. AN INEQUALITY OF GRUSS LIKE VIA VARIANT OF POMPEIU’S MEAN VALUE THEOREM. Konuralp J. Math. 2015;3:29–35.
MLA Sarıkaya, Mehmet Zeki and Hüseyin Budak. “AN INEQUALITY OF GRUSS LIKE VIA VARIANT OF POMPEIU’S MEAN VALUE THEOREM”. Konuralp Journal of Mathematics, vol. 3, no. 1, 2015, pp. 29-35.
Vancouver Sarıkaya MZ, Budak H. AN INEQUALITY OF GRUSS LIKE VIA VARIANT OF POMPEIU’S MEAN VALUE THEOREM. Konuralp J. Math. 2015;3(1):29-35.
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