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: 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.

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

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