scholarly journals On Some Systems of Two Discrete Inequalities of Gronwall Type

1997 ◽  
Vol 208 (2) ◽  
pp. 553-566 ◽  
Author(s):  
Sh. Salem
Keyword(s):  
Discrete Inequalities

scholarly journals Some New Volterra-Fredholm-Type Discrete Inequalities and Their Applications in the Theory of Difference Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-24 ◽  
Author(s):  
Bin Zheng ◽  
Qinghua Feng
Keyword(s):  
Difference Equations ◽  
Fredholm Type ◽  
Qualitative And Quantitative ◽  
Independent Variables ◽  
Discrete Inequalities ◽  
Quantitative Properties ◽  
Two Independent Variables

Some new Volterra-Fredholm-type discrete inequalities in two independent variables are established, which provide a handy tool in the study of qualitative and quantitative properties of solutions of certain difference equations. The established results extend some known results in the literature.

scholarly journals ON LIEB AND THIRRING TYPE DISCRETE INEQUALITIES

1991 ◽  
Vol 22 (2) ◽  
pp. 145-151
Author(s):  
B. G. PACHPATTE
Keyword(s):  
Independent Variables ◽  
Discrete Inequalities ◽  
Forward Differences

Discrete inequalities of the Lieb and Thirring type involving functions of several independent variables and their forward differences are established. The proofs given here are elementary and the results established provide new estimates on these types of inequalities.

scholarly journals New Inequalities of Opial's Type on Time Scales and Some of Their Applications

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
Samir H. Saker
Keyword(s):  
Time Scales ◽  
Second Order ◽  
Dynamic Equations ◽  
Linear Dynamic ◽  
Special Cases ◽  
Discrete Inequalities ◽  
Zeros Of Solutions ◽  
Yield Conditions ◽  
New Inequalities

We will prove some new dynamic inequalities of Opial's type on time scales. The results not only extend some results in the literature but also improve some of them. Some continuous and discrete inequalities are derived from the main results as special cases. The results will be applied on second-order half-linear dynamic equations on time scales to prove several results related to the spacing between consecutive zeros of solutions and the spacing between zeros of a solution and/or its derivative. The results also yield conditions for disfocality of these equations.

scholarly journals New Characterizations of Weights in Hardy and Opial Type Inequalities via Solvability of Dynamic Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
S. H. Saker ◽  
A. G. Sayed ◽  
A. Sikorska-Nowak ◽  
I. Abohela
Keyword(s):  
Time Scales ◽  
Second Order ◽  
Dynamic Equations ◽  
Special Cases ◽  
Discrete Inequalities

In this paper, we prove that the solvability of dynamic equations of second order is sufficient for the validity of some Hardy and Opial type inequalities with two different weights on time scales. In particular, the results give new characterizations of two different weights in inequalities containing Hardy and Opial operators. The main contribution in this paper is the characterizations of weights in discrete inequalities that will be formulated from our results as special cases.

Discrete inequalities of Wirtinger's type for higher differences

1997 ◽  
Vol 1997 (4) ◽  
pp. 312160 ◽  
Author(s):  
Gradimir V Milovanović ◽  
IgorŽ Milovanović
Keyword(s):  
Discrete Inequalities

scholarly journals Chebyshev-Type Integral Inequalities for Continuous Fields of Operators Concerning Khatri–Rao Products and Synchronous Properties

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 422
Author(s):  
Arnon Ploymukda ◽  
Pattrawut Chansangiam
Keyword(s):  
Radon Measure ◽  
Geometric Mean ◽  
Integral Inequalities ◽  
Counting Measure ◽  
Integrable Functions ◽  
Discrete Inequalities ◽  
Finite Space ◽  
Continuous Fields ◽  
Adjoint Operators ◽  
Locally Compact Hausdorff Space

We consider bounded continuous fields of self-adjoint operators which are parametrized by a locally compact Hausdorff space Ω equipped with a finite Radon measure μ . Under certain assumptions on synchronous Khatri–Rao property of the fields of operators, we obtain Chebyshev-type inequalities concerning Khatri–Rao products. We also establish Chebyshev-type inequalities involving Khatri–Rao products and weighted Pythagorean means under certain assumptions of synchronous monotone property of the fields of operators. The Pythagorean means considered here are three classical symmetric means: the geometric mean, the arithmetic mean, and the harmonic mean. Moreover, we derive the Chebyshev–Grüss integral inequality via oscillations when μ is a probability Radon measure. These integral inequalities can be reduced to discrete inequalities by setting Ω to be a finite space equipped with the counting measure. Our results provide analog results for matrices and integrable functions. Furthermore, our results include the results for tensor products of operators, and Khatri–Rao/Kronecker/Hadamard products of matrices, which have been not investigated in the literature.

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