A GENERALIZATION OF OSTROWSKI TYPE INEQUALITY FOR MAPPINGS WHOSE SECOND DERIVATIVES BELONG TO L1(a,b) AND APPLICATIONS

Abstract

In this paper, we will improve and generalize inequality of Ostrowski type for mappings whose second derivatives belong to L 1 (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.

Construction of New Ostrowski’s Type Inequalities By Using Multistep Linear Kernel

“…Qayyum and Husain [5] generalized Ostrowski type integral inequalities to present new estimates. Qayyum et al [6][7][8][9][10][11] provided a generalized form of Ostrowski type Gruss-inequality for twice derivable mappings. Barnett et al [4] stressed another new concept i.e.…”

Some new generalized Ostrowski type inequalities with new error bounds

“…P. Cerone et.al [7] and [8] pointed out an inequality of Ostrowski's type for L ∞ (a, b) , L 1 (a, b) and Lp (a, b) . A. Qayyum et.al [23] and [24] offered Ostrowski' s type inequalities which were the generalization of the inequalities given in [5]. Different researchers [11]- [21] worked on refinement of Ostrowski's type inequalities and its applications.…”

Weighted Ostrowski's Type Integral Inequalities for Mapping Whose Second Derivative is Bounded

“…Then Cerone [2], Dragomir et al [3] and Sarıkaya et al [4] also worked on this inequality. A. Qayyum et al [5][6][7][8][9] worked on generalization of Ostrowski's type inequalities. Different authors worked on the generalization of Ostrowski's type inequalities that are [10], [11] and [12].…”