By introducing a parameter, we establish in this paper a generalization of the companion of Ostrowski-like type integral inequality for mappings whose second derivatives belong to L∞-spaces. Our result in special cases not only recapture known results, but also give a smaller estimator than that of the known results. Some applications to composite quadrature rules in numerical integration and t...

A recently obtained generalization of weighted Montgomery identity is considered and used to obtain the new weighted generalizations of the Čebyšev and Ostrowski inequality.

Different types of mathematical inequalities have been largely analyzed and employed. In this paper, we introduce improvements to some Ostrowski type present their corresponding proofs. The presented proofs are based on applying the celebrated Hayashi inequality certain functions. We provide examples that show these improvements. Illustrations obtained results stated in a probability framework.

Using (1.1), the authors obtained estimations of error for the mid-point, trapezoid, and Simpson quadrature formulae. They also gave applications of the mentioned results in numerical integration and for special means. In this paper, we establish two perturbations of (1.1). Using the perturbations, we derive some new error bounds for the mid-point, trapezoid, and Simpson quadrature formulae. Si...

We generalize cyclic refinements of Jensen’s inequality from a convex function to a higher-order convex function by means of Lagrange–Green’s function and Fink’s identity. We formulate the monotonicity of the linear functionals obtained from these identities utilizing the theory of inequalities for n-convex functions at a point. New Grüssand Ostrowski-type bounds are found for identities associ...

Integration with weight functions is used in countless mathematical problems such as: approximation theory and spectral analysis, statistical analysis and the theory of distributions. The aim of this paper is to establish a new inequality using weight function which generalizes the inequalities of Barnett et al. in 2001 and Rafiq et al. in 2006. We also discuss some other interesting inequaliti...

In this paper we obtain some inequalities related to the generalized triangle and quadratic triangle inequalities for vectors in inner product spaces. Some results that employ the Ostrowski discrete inequality for vectors in normed linear spaces are also obtained.

In this paper we establish a generalisation of the Ostrowski inequality for monotonic functions that also includes various recent results and apply it for quadrature formulae in Numerical Integration.

We consider inequalities which incorporate both Jensen and Ostrowski type inequalities for functions with absolutely continuous n-th derivative. We provide applications of these inequalities for divergence measures. In particular, we obtain inequalities involving higher order χ-divergence.