A generalization of weighted companion of Ostrowski integral inequality for mappings of bounded variation

2020 ◽  
Vol 21 (7-8) ◽  
pp. 667-673
Author(s):  
Mohammad Wajeeh Alomari
Keyword(s):  
Bounded Variation ◽  
Integral Inequality ◽  
Type Inequality ◽  
Quadrature Rule ◽  
Ostrowski Type Inequality

AbstractA weighted companion of Ostrowski type inequality is established. Some sharp inequalities are proved. Application to a quadrature rule is provided.

scholarly journals A new Ostrowski type inequality for functions whose first derivatives are of bounded variation

2016 ◽  
Vol 2 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Hüseyin Budak ◽  
Mehmet Zeki Sarikaya
Keyword(s):  
Bounded Variation ◽  
Quadrature Formula ◽  
Type Inequality ◽  
Integral Inequalities ◽  
Ostrowski Type Inequality ◽  
Type Integral

Abstract In this paper, we establish some new Ostrowski type integral inequalities for mappings whose first derivatives are of bounded variation and quadrature formula is provided

scholarly journals A general Ostrowski type inequality for double integrals

2002 ◽  
Vol 33 (4) ◽  
pp. 319-334
Author(s):  
G. Hanna ◽  
S. S. Dragomir ◽  
P. Cerone
Keyword(s):  
Integral Inequality ◽  
Type Inequality ◽  
Two Dimensions ◽  
One Dimensional ◽  
Ostrowski Type Inequality ◽  
And Function ◽  
Interior Points ◽  
Double Integrals ◽  
Differentiable Mappings

Some generalisations of an Ostrowski Type Inequality in two dimensions for $n-$time differentiable mappings are given. The result is an Integral Inequality with bounded $n-$time derivatives. This is employed to approximate double integrals using one dimensional integrals and function evaluations at the boundary and interior points.

scholarly journals On a new Ostrowski type inequality in two independent variables

2001 ◽  
Vol 32 (1) ◽  
pp. 45-49
Author(s):  
B. G. Pachpatte
Keyword(s):  
Integral Inequality ◽  
Type Inequality ◽  
Discrete Analogue ◽  
Independent Variables ◽  
Ostrowski Type Inequality ◽  
Two Independent Variables

In this note a new integral inequality of Ostrowski type in two independent variables is established. The discrete analogue of the main result is also given.

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 A Korn-type inequality in SBD for functions with small jump sets

2017 ◽  
Vol 27 (13) ◽  
pp. 2461-2484 ◽  
Author(s):  
Manuel Friedrich
Keyword(s):  
Bounded Variation ◽  
Elastic Strain ◽  
Special Functions ◽  
Type Inequality ◽  
Rigid Motion ◽  
Exceptional Set ◽  
Finite Perimeter ◽  
Functions Of Bounded Deformation ◽  
Jump Set

We present a Korn-type inequality in a planar setting for special functions of bounded deformation. We prove that for each function in [Formula: see text] with a sufficiently small jump set the distance of the function and its derivative from an infinitesimal rigid motion can be controlled in terms of the linearized elastic strain outside of a small exceptional set of finite perimeter. Particularly, the result shows that each function in [Formula: see text] has bounded variation away from an arbitrarily small part of the domain.

scholarly journals New Integral Inequalities via Generalized Preinvex Functions

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 296
Author(s):  
Muhammad Tariq ◽  
Asif Ali Shaikh ◽  
Soubhagya Kumar Sahoo ◽  
Hijaz Ahmad ◽  
Thanin Sitthiwirattham ◽  
...  
Keyword(s):  
Integral Inequality ◽  
Type Inequality ◽  
Integral Inequalities ◽  
Power Mean ◽  
Science And Engineering ◽  
Special Means ◽  
Algebraic Properties ◽  
Convexity Theory ◽  
Hölder’S Integral Inequality ◽  
Preinvex Functions

The theory of convexity plays an important role in various branches of science and engineering. The objective of this paper is to introduce a new notion of preinvex functions by unifying the n-polynomial preinvex function with the s-type m–preinvex function and to present inequalities of the Hermite–Hadamard type in the setting of the generalized s-type m–preinvex function. First, we give the definition and then investigate some of its algebraic properties and examples. We also present some refinements of the Hermite–Hadamard-type inequality using Hölder’s integral inequality, the improved power-mean integral inequality, and the Hölder-İşcan integral inequality. Finally, some results for special means are deduced. The results established in this paper can be considered as the generalization of many published results of inequalities and convexity theory.

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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