scholarly journals A Perturbed Ostrowski-Type Inequality on Time Scales for Points for Functions Whose Second Derivatives Are Bounded

2008 ◽  
Vol 2008 (1) ◽  
pp. 597241 ◽  
Author(s):  
Wenjun Liu ◽  
QuốcAnh Ngô ◽  
Wenbing Chen
Keyword(s):  
Time Scales ◽  
Type Inequality ◽  
Ostrowski Type Inequality ◽  
Second Derivatives

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 On Weighted Montgomery Identity for k Points and Its Associates on Time Scales

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Eze R. Nwaeze ◽  
Ana M. Tameru
Keyword(s):  
Weight Function ◽  
Time Scales ◽  
Type Inequality ◽  
Montgomery Identity ◽  
Quantum Calculus ◽  
Ostrowski Type Inequality

The purpose of this paper is to establish a weighted Montgomery identity for k points and then use this identity to prove a new weighted Ostrowski type inequality. Our results boil down to the results of Liu and Ngô if we take the weight function to be the identity map. In addition, we also generalize an inequality of Ostrowski-Grüss type on time scales for k points. For k=2, we recapture a result of Tuna and Daghan. Finally, we apply our results to the continuous, discrete, and quantum calculus to obtain more results in this direction.

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.

Ostrowski Type Inequality for Double Integrals on Time Scales

2008 ◽  
Vol 110 (1) ◽  
pp. 283-288 ◽  
Author(s):  
Umut Mutlu Özkan ◽  
Hüseyin Yildirim
Keyword(s):  
Time Scales ◽  
Type Inequality ◽  
Ostrowski Type Inequality ◽  
Double Integrals
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