scholarly journals A generalized Gronwall-Bellman type delay integral inequality with two independent variables on time scales

2017 ◽  
pp. 1151-1160
Author(s):  
Yuz en Mi
Keyword(s):  
Time Scales ◽  
Integral Inequality ◽  
Independent Variables ◽  
Delay Integral Inequality ◽  
Two Independent Variables

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 dynamic Hilbert-type inequalities in two independent variables involving Fenchel–Legendre transform

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
A. A. El-Deeb ◽  
Saima Rashid ◽  
Zareen A. Khan ◽  
S. D. Makharesh
Keyword(s):  
Time Scales ◽  
Legendre Transform ◽  
Independent Variables ◽  
Hilbert Type ◽  
Two Independent Variables ◽  
New Inequalities

AbstractIn this paper, we establish some dynamic Hilbert-type inequalities in two independent variables on time scales by using the Fenchel–Legendre transform. We also apply our inequalities to discrete and continuous calculus to obtain some new inequalities as particular cases. Our results give more general forms of several previously established inequalities.

scholarly journals On the Generalized Weighted Integral Inequality for Double Integrals

2015 ◽  
Vol 61 (1) ◽  
pp. 169-179 ◽  
Author(s):  
Mehmet Zeki Sarikaya
Keyword(s):  
Integral Inequality ◽  
Independent Variables ◽  
Elementary Analysis ◽  
Weighted Integral ◽  
Function Of Two Variables ◽  
Two Independent Variables ◽  
Double Integrals

Abstract In this paper, we obtain weighted Montgomery’s identities for function of two variables and apply them to give new generalization weighted integral inequality for double integrals involving functions of two independent variables by using fairly elementary analysis.

scholarly journals A NOTE ON TWO DIMENSIONAL INTEGRAL INEQUALITY

1990 ◽  
Vol 21 (3) ◽  
pp. 211-213
Author(s):  
B. G. PACHPATTE
Keyword(s):  
Integral Inequality ◽  
Present Note ◽  
Two Dimensional ◽  
Partial Derivatives ◽  
Independent Variables ◽  
Dimensional Integral ◽  
Two Independent Variables

In the present note we establish a new integral inequality involving a function of two independent variables and its partial derivatives.

scholarly journals Bounds of Double Integral Dynamic Inequalities in Two Independent Variables on Time Scales

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
S. H. Saker
Keyword(s):  
Time Scales ◽  
Unknown Function ◽  
The Other ◽  
Dynamic Equations ◽  
Double Integral ◽  
Independent Variables ◽  
Explicit Bounds ◽  
Quantitative Properties ◽  
The One ◽  
Two Independent Variables

Our aim in this paper is to establish some explicit bounds of the unknown function in a certain class of nonlinear dynamic inequalities in two independent variables on time scales which are unbounded above. These on the one hand generalize and on the other hand furnish a handy tool for the study of qualitative as well as quantitative properties of solutions of partial dynamic equations on time scales. Some examples are considered to demonstrate the applications of the results.

scholarly journals Some New Delay Integral Inequalities in Two Independent Variables on Time Scales

2011 ◽  
Vol 2011 ◽  
pp. 1-18
Author(s):  
Bin Zheng ◽  
Yaoming Zhang ◽  
Qinghua Feng
Keyword(s):  
Time Scales ◽  
Integral Inequalities ◽  
Dynamic Equations ◽  
Boundedness Of Solutions ◽  
Independent Variables ◽  
Discrete Analysis ◽  
Delay Dynamic Equations ◽  
Two Independent Variables

Some new Gronwall-Bellman-type delay integral inequalities in two independent variables on time scales are established, which can be used as a handy tool in the research of boundedness of solutions of delay dynamic equations on time scales. Some of the established results are 2D extensions of several known results in the literature, while some results unify existing continuous and discrete analysis.

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