A generalization of Ostrowski type inequality for mappings whose second derivatives belong to L₁(a,b) and applications

2015/03/28 by Ather Qayyum, Qayyum, Ather, Ibrahima Faye +5
Mathematics · #26D15 #41A55 #41A80 #65C50 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:26D15 #msc:41A55 #msc:41A80 #msc:65C50

paper · pdf · doi:10.48550/arxiv.1503.08283

To Appear in International Journal of Pure and Applied Mathematics

arxiv created 2015/03/28 · arxiv updated 2015/03/31

Abstract

In this paper, we will improve and generalize inequality of Ostrowski type for mappings whose second derivatives belong to L₁(a,b) . Some well known inequalities can be derived as special cases. In addition, perturbed mid-point inequality and perturbed trapezoid inequality are also obtained. The obtained inequalities have immediate applications in numerical integration where new estimates are obtained for the remainder term of the trapezoid and midpoint formula. Applications to some special means are also investigated.

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