Note on Some Nonlinear Integral Inequalities in Two Independent Variables on Time Scales and Applications

2012 ◽  
Vol 5 (3) ◽  
pp. 111-122
Author(s):  
K. Boukerrioua
Keyword(s):  
Time Scales ◽  
Integral Inequalities ◽  
Independent Variables ◽  
Two Independent Variables

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.

scholarly journals Nonlinear Dynamical Integral Inequalities in Two Independent Variables and Their Applications

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Yuangong Sun
Keyword(s):  
Dynamical Systems ◽  
Time Scales ◽  
Integral Inequalities ◽  
Jump Operator ◽  
Qualitative Properties ◽  
Nonlinear Dynamical ◽  
Independent Variables ◽  
Explicit Bounds ◽  
Qualitative Properties Of Solutions ◽  
Two Independent Variables

In this paper, we investigate some nonlinear dynamical integral inequalities involving the forward jump operator in two independent variables. These inequalities provide explicit bounds on unknown functions, which can be used as handy tools to study the qualitative properties of solutions of certain partial dynamical systems on time scales pairs.

scholarly journals Explicit Bounds to Some New Gronwall-Bellman-Type Delay Integral Inequalities in Two Independent Variables on Time Scales

2011 ◽  
Vol 2011 ◽  
pp. 1-25 ◽  
Author(s):  
Fanwei Meng ◽  
Qinghua Feng ◽  
Bin Zheng
Keyword(s):  
Time Scales ◽  
Integral Inequalities ◽  
Dynamic Equations ◽  
Qualitative And Quantitative ◽  
Independent Variables ◽  
Delay Dynamic Equations ◽  
Explicit Bounds ◽  
Quantitative Properties ◽  
Two Independent Variables

Some new Gronwall-Bellman-type delay integral inequalities in two independent variables on time scales are established, which provide a handy tool in the research of qualitative and quantitative properties of solutions of delay dynamic equations on time scales. The established inequalities generalize some of the results in the work of Zhang and Meng 2008, Pachpatte 2002, and Ma 2010.

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.

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