Some inequalities of Ostrowski and Grüss type for triple integrals on time scales

Article Sidebar

PDF
Published: Dec 31, 2011
DOI: https://doi.org/10.5556/j.tkjm.42.2011.685
Keywords:
Ostrowski and Grüss type inequality Triple integral Time scale.

Main Article Content

Nazir Ahmad Mir
COMSATS Insttitute of Information Technology, Department of Mathematics, Park Road, Shehzad Town, 44000 ISLAMABAD, Pakistan
Roman Ullah
Department ofMathematics, COMSATS Institute of Information Technology, Islamabad, Pakistan.

Abstract

In this paper, we establish some inequalities of Ostrowski and Grüss type for triple integrals on arbitrary time scales involving three functions and their partial derivatives. We also discuss the discrete Ostrowski and Grüss type inequalities for triple sumon time scale.

Article Details

How to Cite
Mir, N. A., & Ullah, R. (2011). Some inequalities of Ostrowski and Grüss type for triple integrals on time scales. Tamkang Journal of Mathematics, 42(4), 415–426. https://doi.org/10.5556/j.tkjm.42.2011.685
Issue
Vol. 42 No. 4 (2011)
Section
Papers
Author Biography

Nazir Ahmad Mir, COMSATS Insttitute of Information Technology, Department of Mathematics, Park Road, Shehzad Town, 44000 ISLAMABAD, Pakistan

Professor of Mathematics

Department of Mathematics

References

R. Agarwal, M. Bohner and A. Peterson, textit{Inequalities on time scales:a survey, Inequal. Appl., 4(2001), 535--557.

Farooq Ahmad, Arif Rafiq and Nazir Ahmad Mir, Weighted Ostrowski-Gruss type inequality for differentiable mappings}, Glob. J. Pure Appl. Math., No.2,(2006), 147--154.

M. Bohner and A. Peterson, Dynamic Equations on Time Scales, An Introduction with Applications, Boston, MA. Birkhaser Boston Inc., 2001.

M. Bohner and T. Mathews, The Gruss inequality on time scales, Commun. Math. Anal., 3(2007), 1--8.

M. Bohner and G. Sh. Guseinov, Double integral calculus of variations on time scales, Comput. Math. Appl., 54(2007), 45--57.

S. S. Dragomir and Young-Ho Kim, On certian new integral inequalities and their applications, J. Ineq. Pure Appl. Math., 3(2002), Article 65.

S. S. Dragomir and A. Sofo, An integral inequality for twice differentiable mappings and applications, Tamkang Journal of Mathematics, 31(2000), 257--266.

G. Gruss. Uber das Maximum des absoluten Betrages von, Math. Z., 39 (1935), 215--226.

S. Hilger, Ein Ma$beta$kettenkul mit Anwendung auf Zentrumsmannigfaltigkeiten, PhD thesis, Universitat Wurzburg, 1988.

Wenjun Liu and Quoc-Anh Ngo, An Ostrowski-Gruss type inequality on time scales, Comput. Math. Appl., 58(2009), 1207--1210.

W. J. Liu, Q. A. Ngo and W. B. Chen, Ostrowski type inequalities on time scales for double integrals, Acta Appl. Math., 110(2010), 477--497.

N. A. Mir and A. Rafiq, A note on Ostrowski like inequalities in L$%_{1}(a,b)$ spaces, Gen. Math., 14 (2006), 23--30.

N. A. Mir, A. Rafiq and F. Ahmad, Weighted Ostrowski type inequality for differentiable mappings whose derivative belong to L$_{infty }(a,b)$, Gen. Math., 14(2006), 27--38.

Nazir Ahmad Mir, Arif Rafiq and Farooq Ahmad, Generalization of integral inequalities for functions whose modulus of nth derivatives are convex, Gen. Math., 14(2007), 67--92.

Nazir Ahmad Mir, Arif Rafiq and Muhammad Rizwan, Ostrowski-Gruss cebysew type inequalities for functions whose modulus for second derivatives are convex, Gen. Math., 16(2008), 111--134.

A. Ostrowski, Uber die Absolutabweichung einer differentienbaren Funktionen von ihren Integralmittelwert, Comment. Math. Helv., 10(1938), 226--227.

U. M. Ozkan and H. Yildirim, Ostrowski type inequality for double integrals on time scales, Acta Appl. Math., 10(2010), 283--288.

B. G. Pachpatte, On Gruss type inequality for double integrals, J. Math. Anal. Appl., 267(2002), 454--459.

B. G. Pachpatte, New Inequalities of Ostrowski and Gruss type for triple integrals, Tamkang J. Math., 40 (2009),117-127.

Umut Mutlu Ozkan and Huseyin Yildrim, Gruss type inequalities for doubleintegrals on time scales, Comput. Math. Appl., 57(2009), 436--444.

A. Rafiq, N. A. Mir and Fiza Zafar, A generalized Ostrowski-Gruss type inequality for twice differentiable mappings in Euclidean norm, Gen. Math., 16(2008), 51--72.

Arif Rafiq, Nazir Ahmad Mir, and Fiza Zafar, A generalized Ostrowski type inequality for a random variable whose probability density function belongs to $L_{infty }left[ a,bright] $, Demonstratio Math., 41(2008), 723-732.

A. Sofo, Double integral inequalities based on multi-branch Peano kernels, Math. Ineq. & Appl., 5(2002), 491--504.