scholarly journals Perturbations of an Ostrowski type inequality and applications

2002 ◽  
Vol 32 (8) ◽  
pp. 491-500 ◽  
Author(s):  
Nenad Ujević
Keyword(s):  
Numerical Integration ◽  
Error Bounds ◽  
Type Inequality ◽  
Quadrature Rules ◽  
Ostrowski Type Inequality ◽  
Better Than

Two perturbations of an Ostrowski type inequality are established. New error bounds for the mid-point, trapezoid, and Simpson quadrature rules are derived. These error bounds can be much better than some recently obtained bounds. Applications in numerical integration are also given.

scholarly journals AN OSTROWSKI TYPE INEQUALITY FOR TWICE DIFFERENTIABLE MAPPINGS AND APPLICATIONS

2016 ◽  
Vol 21 (4) ◽  
pp. 522-532 ◽  
Author(s):  
Samet Erden ◽  
Huseyin Budak ◽  
Mehmet Zeki Sarikaya
Keyword(s):  
Numerical Integration ◽  
Type Inequality ◽  
Special Means ◽  
Ostrowski Type Inequality ◽  
Second Derivatives ◽  
Differentiable Mappings

We establish an Ostrowski type inequality for mappings whose second derivatives are bounded, then some results of this inequality that are related to previous works are given. Finally, some applications of these inequalities in numerical integration and for special means are provided.

Two Sharp Perturbed Midpoint Inequalities

2014 ◽  
Vol 472 ◽  
pp. 527-531
Author(s):  
Yan Xia Shi ◽  
Yu Min Tao ◽  
Yu Pan
Keyword(s):  
Numerical Integration ◽  
Error Bounds ◽  
Kernel Functions ◽  
Quadrature Rules

In this study, two new sharp perturbed midpoint inequalities are proved by establishing proper kernel functions. These results enlarge applicability of the corresponding quadrature rules with respect to the obtained error bounds. Applications in numerical integration are also given.

scholarly journals Inequalities and Approximations for the Finite Hilbert Transform: A Survey of Recent Results

2018 ◽  
Author(s):  
Silvestru Sever Dragomir
Keyword(s):  
Numerical Integration ◽  
Explicit Form ◽  
Bounded Variation ◽  
Hilbert Transform ◽  
Error Bounds ◽  
Higher Order ◽  
Quadrature Rules ◽  
Absolutely Continuous ◽  
Finite Hilbert Transform

In this paper we survey some recent results due to the author concerning various inequalities and approximations for the finite Hilbert transform of a function belonging to several classes of functions, such as: Lipschitzian, monotonic, convex or with the derivative of bounded variation or absolutely continuous. More accurate estimates in the case that the higher order derivatives are absolutely continuous, are also provided. Some quadrature rules with error bounds are derived. They can be used in the numerical integration of the finite Hilbert transform and, due to the explicit form of the error bounds, enable the user to predict a priory the accuracy.

New generalized 2D Ostrowski type inequalities on time scales with k2 points using a parameter

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3155-3169 ◽  
Author(s):  
Seth Kermausuor ◽  
Eze Nwaeze
Keyword(s):  
Numerical Analysis ◽  
Time Scales ◽  
Type Inequality ◽  
Dimensional Case ◽  
Multiple Points ◽  
Quantum Calculus ◽  
Independent Variables ◽  
Ostrowski Type Inequality ◽  
Two Independent Variables

Recently, a new Ostrowski type inequality on time scales for k points was proved in [G. Xu, Z. B. Fang: A Generalization of Ostrowski type inequality on time scales with k points. Journal of Mathematical Inequalities (2017), 11(1):41-48]. In this article, we extend this result to the 2-dimensional case. Besides extension, our results also generalize the three main results of Meng and Feng in the paper [Generalized Ostrowski type inequalities for multiple points on time scales involving functions of two independent variables. Journal of Inequalities and Applications (2012), 2012:74]. In addition, we apply some of our theorems to the continuous, discrete, and quantum calculus to obtain more interesting results in this direction. We hope that results obtained in this paper would find their place in approximation and numerical analysis.

scholarly journals New error bounds for linear complementarity problems of Σ-SDD matrices and SB-matrices

2019 ◽  
Vol 17 (1) ◽  
pp. 1599-1614
Author(s):  
Zhiwu Hou ◽  
Xia Jing ◽  
Lei Gao
Keyword(s):  
Linear Algebra ◽  
Error Bound ◽  
Linear Complementarity Problem ◽  
Error Bounds ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Numerical Examples ◽  
Numer Algor ◽  
Better Than

Abstract A new error bound for the linear complementarity problem (LCP) of Σ-SDD matrices is given, which depends only on the entries of the involved matrices. Numerical examples are given to show that the new bound is better than that provided by García-Esnaola and Peña [Linear Algebra Appl., 2013, 438, 1339–1446] in some cases. Based on the obtained results, we also give an error bound for the LCP of SB-matrices. It is proved that the new bound is sharper than that provided by Dai et al. [Numer. Algor., 2012, 61, 121–139] under certain assumptions.

scholarly journals Revisited Optimal Error Bounds for Interpolatory Integration Rules

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
François Dubeau
Keyword(s):  
Error Bounds ◽  
Error Term ◽  
Quadrature Rules ◽  
Optimal Error ◽  
Integration By Parts ◽  
Integration Rules

We present a unified way to obtain optimal error bounds for general interpolatory integration rules. The method is based on the Peano form of the error term when we use Taylor’s expansion. These bounds depend on the regularity of the integrand. The method of integration by parts “backwards” to obtain bounds is also discussed. The analysis includes quadrature rules with nodes outside the interval of integration. Best error bounds for composite integration rules are also obtained. Some consequences of symmetry are discussed.

scholarly journals A new Ostrowski type inequality involving integral means over end intervals

2002 ◽  
Vol 33 (2) ◽  
pp. 109-118
Author(s):  
P. Cerone
Keyword(s):  
Type Inequality ◽  
Current Development ◽  
Ostrowski Inequality ◽  
Integral Means ◽  
Entire Interval ◽  
Ostrowski Type Inequality ◽  
Current Article ◽  
Chebychev Functional

The Ostrowski inequality expresses bounds on the deviation of a function from its integral mean. 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. Perturbed expressions are also determined via the Chebychev functional. A variety of earlier results are recaptured as particular instances of the current development.

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