Weighted ?eby》ev-Ostrowski Type Inequalities Involving Functions Whose First Derivatives Belong to a Spaces of the Functions

Arif Rafiq; Nazir Ahmad Mir; Farooq Ahmad

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2007 > 28(7): 805-810

Arif Rafiq, Nazir Ahmad Mir, Farooq Ahmad. Weighted ?eby》ev-Ostrowski Type Inequalities Involving Functions Whose First Derivatives Belong to a Spaces of the Functions[J]. Applied Mathematics and Mechanics, 2007, 28(7): 805-810.

Citation:

PDF( 258 KB)

Weighted ?eby》ev-Ostrowski Type Inequalities Involving Functions Whose First Derivatives Belong to a Spaces of the Functions

1.
Mathematics Department, COMSATS Institute of Information Technology, Plot # 30, Sector H-8/1, Islamabad 44000, Pakistan;

Received Date: 2006-08-17
Rev Recd Date: 2007-03-16
Publish Date: 2007-07-15

Abstract

Abstract

On account of the famous ?eby》ev inequality, a rich theory has appeared in some literature. Some new weighted ?eby》ev type integral inequalities via certain integral inequalities for functions whose first derivatives belong to a space of the functions are established. The proofs are of independent interest and provide new estimates on these types of inequalities.
- ?eby》ev type inequality,
- space of the function,
- absolutely continuous function,
- weight function

FullText(HTML)

References(14)

References

[1]	ebyev P L. Sur les expressions approximatives des integrals par les auters prises entre les memes limites[J].Proc Math Soc Charkov,1882,2:93-98.
[2]	Pecaric J E, Porchan F, Tong Y.Convex Functions, Partial Orderings and Statistical Applications[M]. San Diego: Academic Press, 1992.
[3]	Dragomir S S , Rassias Th M.Ostrowski Type Inequalities and Applications in Numerical Integration[M].USA:Springer, 2002, 504.
[4]	Heing H P, Maligranda L.ebyev inequality in function spaces[J].Real Analysis Exchange,1991/1992,17(1)：211-247.
[5]	Kwong M K, Zettl A.Norm Inequalities for Derivatives and Difference[M].New York/Berlin : Springer -Verlag,1980.
[6]	Mitrinovic D S, Pecaric J E, Fink A M.Classical and New Inequalities in Analysis[M]. Dordrecht: Kluwer Academic Publishers, 1993.
[7]	Pachpatte B G. On Trapezoid and Gruss like integral inequalities[J].Tamkang J Math,2003,34(4):365-369.
[8]	Pachpatte B G. On Ostrowski-Grüss-ebyev type inequalities for functions whose modulus of derivatives are convex[J].J Inequal Pure Appl Math,2005,6(4):128.
[9]	Pachpatte B G. On ebyev type inequalities involving functions whose derivatives belong to Lp spaces[J].J Inequal Pure Appl Math,2006,7(2): 58.
[10]	Varosanec S. History, generalizations and applied unified treatments of two Ostrowski inequalities[J].J Inequal Pure Appl Math,2004,5(2):23.
[11]	Dragomir S S. On simpson's quadrature formula for differentiable mappings whose derivatives belong to Lp spaces and applications[J].RGMIA Res Rep Coll,1998,1(2):89-96.
[12]	Dragomir S S, Barnett N S. An ostrowski type inequality for mappings whose second derivatives are bounded and applications[J].RGMIA Res Rep Coll,1998,1(2):69-77.
[13]	Dragomir S S, Wang S. A new inequality of Ostrowski's type in Lp norm[J].Indian J Math,1998,40(3):299-304.
[14]	Mitrinovic D S,Pecaric J E, Fink A M.Inequalities Involving Functions and Their Integrals and Derivatives[M].Dordrecht: Kluwer Academic Publishers, 1991.