arXiv subjects

Ather Qayyum

Publications and source records attributed to Ather Qayyum.

4 recordsLinked to original sources

arXiv2015

Some New Generalized Results on Ostrowski Type Integral Inequalities With Application

The aim of this paper is to establish some new inequalities similar to the Ostrowski's inequalities which are more generalized than the inequalities of Dragomir and Cerone. The current article obtains bounds for the deviation of a function from a combination of integral means over the end intervals covering the entire interval. Some new purterbed results are obtained. Application for cumulative distribution function is also discussed.

math.CA↗

arXiv2015

A generalization of Ostrowski type inequality for mappings whose second derivatives belong to L$_{1}\left(a,b\right) $ and applications

In this paper, we will improve and generalize inequality of Ostrowski type for mappings whose second derivatives belong to L$_{1}\left(a,b\right) $ . 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.

math.CA↗

arXiv2014

A Weighted Ostrowski Type inequality for L$_{1}\left[ a,b\right] $ and applications

The aim of this paper is to obtain some generalized weighted Ostrowski inequalities for differentiable mappings. Some well known inequalities can be derived as special cases of the inequalities obtained here. In addition, perturbed mid-point inequality and perturbed trapezoid inequality are also obtained. The inequalities obtained here have direct applications in Numerical Integration, Probability Theory, Information Theory and Integral Operator Theory. Some of these applications are discussed.

math.CA↗

arXiv2014

Weighted Ostrowski Type inequality Involving Integral Means

The ostrowski inequality expresses bounds on the deviation of a function from its integral mean. The aim of this paper is to establish a new inequality using weight function which generalizes the inequalities of Dragomir, Wang and Cerone .The current article obtains bounds for the deviation of a function from a combination of 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 are also discussed.

math.CA↗