A.M. Ostrowski in 1951 gave two well-known upper bounds for the spectral radius of nonnegative matrices. However, the bounds are not of much practical use because they all involve a parameter α in the interval [0, 1], and it is not easy to decide the optimum value of α. In this paper, their equivalent forms which can be computed with the entries of matrix and without having to minimize the expr...

This research focuses on the Ostrowski–Mercer inequalities, which are presented as variants of Jensen’s inequality for differentiable convex functions. The main findings were effectively composed functions and their properties. results directed by Riemann–Liouville fractional integral operators. Furthermore, using special means, q-digamma modified Bessel functions, some applications acquired ob...

In this paper, we present fourth-order families of new variants of King’s fourth-order family of methods for solving nonlinear equations. Per iteration the obtained methods require two evaluations of the given function and one of its first derivative. The classical Traub–Ostrowski method is obtained as a special variant of King’s method. Several numerical examples are given to illustrate the ef...

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...

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.

In the present paper, the notion of generalized $(r;g,s,m,varphi)$-preinvex function is applied to establish some new generalizations of Ostrowski type integral inequalities via Caputo $k$-fractional derivatives. At the end, some applications to special means are given.

In this paper, we have obtained weighted versions of Ostrowski, Čebysev and Grüss type inequalities for conformable fractional integrals which is given by Katugompola. By using the Katugampola definition for conformable calculus, the present study confirms previous findings and contributes additional evidence that provide the bounds for more general functions.