The main purpose of this paper is to use a Grüss type inequality for RiemannStieltjes integrals to obtain a sharp integral inequality of Ostrowski-Grüss type for functions whose first derivative are functions of Lipschitizian type and precisely characterize the functions for which equality holds.

Some Ostrowski and trapezoid type inequalities for the Stieltjes integral in the case of Lischitzian integrators for both Hölder continuous and monotoonic integrals are obtained. The dual case is also analysed. Applications for the midpoint rule are pointed out as well.

Inequalities are obtained for quadrature rules in terms of upper and lower bounds of the first derivative of the integrand. Bounds of Ostrowski type quadrature rules are obtained and the classical Iyengar inequality for the trapezoidal rule is recaptured as a special case. Applications to numerical integration are demonstrated.

We consider the Steffensen–Hayashi inequality and remainder identity for V-fractional differentiable functions involving six parameters truncated Mittag–Leffler function Gamma function. In view of these, we obtain some integral inequalities Steffensen, Hermite–Hadamard, Chebyshev, Ostrowski, Grüss type to calculus.

In this paper, we obtain new Ostrowski type inequalities by using the extended version of Montgomery identity and Green’s functions. We also give estimations difference between two integral means.

The aim of this paper is to correct results from the published paper: A companion Ostrowski Type Integral Inequality Using a 5-Step Kernel with Some Applications, Filomat 30:13 (2016), 3601-3614.

Some generalized Ostrowski-type integral inequalities for r−times differentiable functions whose absolute values are MT−convex have been discussed. Moreover, some applications on special bivariate means obtained.

In this paper we obtain some weighted Čebyšev-Ostrowski type integral inequalities on time scales involving functions whose first derivatives belong to Lp (a,b) (1 p ∞) . We also give some other interesting inequalities as special cases. Mathematics subject classification (2010): 26D15, 26E70.

A one-parameter 4-point sixteenth-order King-type family of iterative methods which satisfy the famous Kung-Traub conjecture is proposed. The convergence of the family is proved, and numerical experiments are carried out to find the best member of the family. In most experiments, the best member was found to be a sixteenth-order Ostrowski-type method.

Some Ostrowski type inequalities are given for the Stieltjes integral where the integrand is absolutely continuous while the integrator is of bounded variation. The case when |f ′| is convex is explored. Applications for the midpoint rule and a generalised trapezoid type rule are also presented.