On New Weighted Ostrowski Type inequalities Involving Integral Means over End Intervals and Application

A. Qayyum¹, M. Shoaib² and I. Faye^1,

¹Department of Fundamental and Applied Sciences, Universiti Teknologi Petronas, Malaysia

²Department of Mathematics, University of Hail, 2440, Saudi Arabia

Cite this paper:
A. Qayyum, M. Shoaib and I. Faye. On New Weighted Ostrowski Type inequalities Involving Integral Means over End Intervals and Application. Turkish Journal of Analysis and Number Theory. 2015; 3(2):61-67. doi: 10.12691/tjant-3-2-5

Abstract

The aim of this paper is to establish new inequalities using weight function which generalizes the inequalities of Dragomir, Wang and Cerone. In this article we obtain bounds for the deviation of a function from a combination of weighted integral means over the end intervals covering the entire interval. A variety of earlier results are recaptured as particular instances of the current development. Applications for cumulative distribution function is also discussed.

Keywords:
ostrowski inequality weight function weighted integral mean

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References:

[1]	P. Cerone, A new Ostrowski type inequality involving integral Means over end intervals, Tamkang Journal Of Mathematics Volume 33, Number 2, 2002.
[2]	P. Cerone and S.S. Dragomir, Trapezoidal type rules from an inequalities point of view, Handbook of Analytic-Computational Methods in Applied Mathematics, CRC Press N.Y. (2000).
[3]	X. L. Cheng, Improvement of some Ostrowski-Grüss type inequalities, Comput. Math. Appl. 42 (2001), 109 114.
[4]	S. S. Dragomir and N. S. Barnett, An Ostrowski type inequality for mappings whose second derivatives are bounded and applications, RGMIA Research Report Collection, V.U.T., 1(1999), 67-76.
[5]	S. S. Dragomir and S. Wang, A new inequality Ostrowski’s type in Lp-norm, Indian J. of Math. 40 (1998), 299-304.
[6]	S. S. Dragomir and S. Wang, A new inequality Ostrowski’s type in L1-norm and applications to some special means and some numerical quadrature rules, Tamkang J. of Math. 28(1997), 239-244.
[7]	S. S. Dragomir and S. Wang, An inequality Ostrowski-Grüss type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules, Computers Math. Applic. 33(1997), 15-22.
[8]	S. S. Dragomir and S. Wang, Applications of Ostrowski’s inequality to the estimation of error bounds for some special means and to some numerical quadrature rules, Appl. Math.Lett. 11(1998), 105-109.
[9]	S. S. Dragomir and S. Wang, An inequality of Ostrowski-Grüs type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules, Comput. Math. Appl., 33 (11), 15-20, (1997).
[10]	Z. Liu, Some companions of an Ostrowski type inequality and application, J. Inequal. in Pure and Appl. Math, 10(2), 2009, Art. 52.
[11]	G. V. Milovanovicˊ and J. E. Pecaricˊ, On generalization of the inequality of A. Ostrowski and some related applications, Univ. Beograd Publ. Elektrotehn. Fak. Ser. Mat. Fiz. (544-576), 155-158, (1976).
[12]	D. S. Mitrinovicˊ, J. E. Pecaricˊ and A. M. Fink, Inequalities for Functions and Their Integrals and Derivatives, Kluwer Academic Publishers, 1994.
[13]	A.Ostrowski, Uber die Absolutabweichung einer di erentienbaren Funktionen von ihren Integralimittelwert, Comment. Math. Hel. 10 (1938), 226-227.
[14]	A. Qayyum, M. Shoaib, A. E. Matouk, and M. A. Latif, On New Generalized Ostrowski Type Integral inequalities, Abstract and Applied Analysis, Volume 2014, Article ID 275806.
[15]	A. Qayyum, M. Shoaib, and I. Faye, Some New Generalized Results on Ostrowski Type Integral Inequalities With Application, Journal of computational analysis and applications, vol. 19, No.4, 2015.
[16]	A. Qayyum, I. Faye, M. Shoaib, M.A. Latif, A Generalization of ostrowski type inequality for mappings whose second derivatives belong to L1(a,b) and applications, International Journal of Pure and Applied Mathematics, 98 (2) 2015, 169-180.
[17]	A. Qayyum, M. Shoaib, M.A. Latif, A Generalized inequality of Ostrowski type for twice differentiable bounded mappings and applications, Applied Mathematical Sciences, Vol. 8, 2014, (38), 1889-1901.