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 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.

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 New weighted inequalities for higher order derivatives and applications

Filomat ◽  
2018 ◽  
Vol 32 (12) ◽  
pp. 4419-4433 ◽  
Author(s):  
Samet Erden ◽  
Mehmet Sarikaya ◽  
Huseyin Budak
Keyword(s):  
Type Inequality ◽  
Random Variables ◽  
Higher Order ◽  
Weighted Inequalities ◽  
Absolute Value ◽  
Ostrowski Type Inequality ◽  
New Inequalities ◽  
Differentiable Mappings

We establish a new Ostrowski type inequality for (n+1)-times differentiable mappings which are bounded. Then, some new inequalities of Hermite-Hadamard type are obtained for functions whose (n+1) th derivatives in absolute value are convex. Spacial cases of these inequalities reduce some well known inequalities. With the help of obtained inequalities, we give applications for the kth-moment of random variables.

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.

scholarly journals An Ostrowski type inequality in two dimensions using the three point rule

2000 ◽  
Vol 42 ◽  
pp. 671 ◽  
Author(s):  
G. Hanna ◽  
P. Cerone ◽  
J. Roumeliotis
Keyword(s):  
Type Inequality ◽  
Two Dimensions ◽  
Ostrowski Type Inequality

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

Structure and function of neural networks in the retina

1988 ◽  
Vol 46 ◽  
pp. 26-27
Author(s):  
Peter Sterling
Keyword(s):  
Ganglion Cells ◽  
Three Dimensional ◽  
Structure And Function ◽  
Synaptic Connections ◽  
Visual Axis ◽  
One Dimensional ◽  
Cat Retina ◽  
Ultrathin Sections ◽  
And Function ◽  
Insight Into

The synaptic connections in cat retina that link photoreceptors to ganglion cells have been analyzed quantitatively. Our approach has been to prepare serial, ultrathin sections and photograph en montage at low magnification (˜2000X) in the electron microscope. Six series, 100-300 sections long, have been prepared over the last decade. They derive from different cats but always from the same region of retina, about one degree from the center of the visual axis. The material has been analyzed by reconstructing adjacent neurons in each array and then identifying systematically the synaptic connections between arrays. Most reconstructions were done manually by tracing the outlines of processes in successive sections onto acetate sheets aligned on a cartoonist's jig. The tracings were then digitized, stacked by computer, and printed with the hidden lines removed. The results have provided rather than the usual one-dimensional account of pathways, a three-dimensional account of circuits. From this has emerged insight into the functional architecture.

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 Markov chain approximation of one-dimensional sticky diffusions

2021 ◽  
Vol 53 (2) ◽  
pp. 335-369
Author(s):  
Christian Meier ◽  
Lingfei Li ◽  
Gongqiu Zhang
Keyword(s):  
Markov Chain ◽  
Approximate Solutions ◽  
Price Model ◽  
One Dimensional ◽  
Markov Chain Approximation ◽  
Alternative Approaches ◽  
Second Order Convergence ◽  
Chain Approximation ◽  
Matrix Exponentials ◽  
Interior Points

AbstractWe develop a continuous-time Markov chain (CTMC) approximation of one-dimensional diffusions with sticky boundary or interior points. Approximate solutions to the action of the Feynman–Kac operator associated with a sticky diffusion and first passage probabilities are obtained using matrix exponentials. We show how to compute matrix exponentials efficiently and prove that a carefully designed scheme achieves second-order convergence. We also propose a scheme based on CTMC approximation for the simulation of sticky diffusions, for which the Euler scheme may completely fail. The efficiency of our method and its advantages over alternative approaches are illustrated in the context of bond pricing in a sticky short-rate model for a low-interest environment and option pricing under a geometric Brownian motion price model with a sticky interior point.

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