NEW INTEGRAL INEQUALITIES ON TIME SCALES WITH APPLICATIONS TO THE CONTINUOUS AND DISCRETE CALCULUS

TitleNEW INTEGRAL INEQUALITIES ON TIME SCALES WITH APPLICATIONS TO THE CONTINUOUS AND DISCRETE CALCULUS
Publication TypeJournal Article
Year of Publication2018
AuthorsNWAEZE, R
Secondary TitleCommunications in Applied Analysis
Volume22
Issue1
Start Page1
Pagination18
Date Published09/2017
Type of Workscientific: mathematics
ISBN Number1083-2564
AMS26D10, 26D15, 54C30
Abstract

In this paper, we present some new weighted Ostrowski and Ostrowski-Grüss type inequalities on time scales. Our results generalize many other results in the literature. Besides generalization, we also obtain some interesting inequalities by considering special cases of time scales.

URLhttp://www.acadsol.eu/en/articles/22/1/1.pdf
DOI10.12732/caa.v22i1.1
Short TitleNEW INTEGRAL INEQUALITIES ON TIME SCALES...
Alternate JournalCAA
Refereed DesignationRefereed
Full Text

REFERENCES

[1] M. Bohner, A. Peterson, Dynamic equations on time scales, Birkhäuser Boston, Boston, MA 2001.
[2] M. Bohner, A. Peterson, Advances in Dynamic Equations on Time Series, Birkhäuser Boston, Boston, MA 2003.
[3] M. Bohner, T. Matthews, Ostrowski inequality on time scales, Journal of Inequalities in Pure and Applied Mathematics, 6 (2008), Article 6.
[4] S. S. Dragomir, S. Wang, An inequality of Ostrowski-Grüss type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules, Computer & Mathematics with Applications, 33 (1997), 16-20.
[5] S. S. Dragomir, Grüss inequality in inner product spaces, Gazette of the Australian Mathematical Society, 26(2) (1999), 66-70. 
[6] S. Hilger, Ein Maβkettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten, Ph.D. thesis, Universität Würzburg, Würzburg, Germany 1988.
[7] S. Kermausuor, E. R. Nwaeze, D. F. M. Torres, Generalized weighted Ostrowski and Ostrowski-Grüss type inequalities on time scales via a parameter function, Journal of Mathematical Inequalities, arXiv:1706.09227v1.
[8] W. J. Liu, Q. A. Ngô, A new generalization of Ostrowski type inequality on time scales, An St Univ Ovidius Constanta, 17(2) (2009), 101-114.
[9] W. J. Liu, A. Tuna, Y. Jiang, New weighted Ostrowski and Ostrowski-Güss type inequalities on time scales, Analele Stiintifice ale Universitatii Al I Cuza din lasi-Matematica, (2014). DOI: 10.2478/aicu-2013-0002
[10] W. J. Liu, A. Tuna, Y. Jiang, On weighted Ostrowski type, Trapezoid type, Grüss type and Ostrowski-Grüss like inequalities on time scales, Applicable Analysis, 93(3) (2014), 551-571.
[11] W. J. Liu, Q. A. Ngô, An Ostrowski-Grüss type inequality on time scales, arXiv:0804.3231v1.
[12] E. R. Nwaeze, A new weighted Ostrowski type inequality on arbitrary time scale, Journal of King Saud University - Science, 29(2) (2017) 230-234.
[13] E. R. Nwaeze, Generalized weighted trapezoid and Grüss type inequalities on time scales, Australian Journal of Mathematical Analysis and Applications, 11(1) (2017), Article 4.
[14] E. R. Nwaeze, A. M. Tameru, On weighted Montgomery identity for k points and its associates on time scales, Abstract and Applied Analysis, (2017) Art. ID 5234181.
[15] A. Tuna, D. Daghan, Generalization of Ostrowski and Ostrowski-Grüss type inequalities on time scales, Computer & Mathematics with Applications, 60 (2010), 803-811.
[16] G. Xu, Z. B. Fang, A new Ostrowski type inequality on time scales, Journal of Mathematical Inequalities, 10(3) (2016), 751-760.