scholarly journals Some New Volterra-Fredholm-Type Nonlinear Discrete Inequalities with Two Variables Involving Iterated Sums and Their Applications

2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Run Xu
Keyword(s):  
Qualitative Analysis ◽  
Difference Equations ◽  
Fredholm Type ◽  
Discrete Inequalities

Some generalized discrete Volterra-Fredholm-type inequalities were developed, which can be used as effective tools in the qualitative analysis of the solution to difference equations.

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.

Qualitative analysis for two fractional difference equations

2020 ◽  
Vol 9 (1) ◽  
pp. 265-272
Author(s):  
Mohammed B. Almatrafi ◽  
Marwa M. Alzubaidi
Keyword(s):  
Qualitative Analysis ◽  
Exact Solutions ◽  
Difference Equations ◽  
Global Attractivity ◽  
Fractional Difference ◽  
Rational Difference Equations ◽  
Fractional Difference Equations ◽  
Special Cases

AbstractSome difference equations are generally studied by investigating their long behaviours rather than their exact solutions. The proposed equations cannot be solved analytically. Hence, this article discusses the main qualitative behaviours of two rational difference equations. Some appropriate hypotheses are examined and given to show the local and global attractivity. Special cases from the considered equations are solved analytically. The periodicity is also proved in this work. We also illustrate the achieved results in some 2D figures.

scholarly journals A sharp upper bound for discrete inequalities of Gronwall-Bellman type

1989 ◽  
Vol 2 (2) ◽  
pp. 113-116
Author(s):  
E. Thandapani
Keyword(s):  
Exact Solution ◽  
Difference Equations ◽  
Upper Bound ◽  
Discrete Equation ◽  
System Of Difference Equations ◽  
Discrete Inequality ◽  
Discrete Inequalities

A sharp upper bound is given for solutions of a discrete inequality of the Gronwall-Bellman type. The bound, which is the exact solution of the corresponding discrete equation, is obtained by reducing the equation to a system of difference equations.

scholarly journals Some new Volterra-Fredholm type discrete inequalities with four iterated infinite sums with applications

2017 ◽  
pp. 495-510 ◽  
Author(s):  
Sabir Hussain ◽  
Shaista Amat ur Rehman ◽  
Humaira Khalid ◽  
Qing-Hua Ma
Keyword(s):  
Fredholm Type ◽  
Discrete Inequalities ◽  
Infinite Sums

scholarly journals Some new Volterra-Fredholm type discrete inequalities with four iterated infinite sums with applications

2017 ◽  
pp. 495-510
Author(s):  
Sabir Hussain ◽  
Shaista Amat ur Rehman ◽  
Humaira Khalid ◽  
Qing-Hua Ma
Keyword(s):  
Fredholm Type ◽  
Discrete Inequalities ◽  
Infinite Sums

Two Iterative Discrete Inequalities

2014 ◽  
Vol 889-890 ◽  
pp. 579-582
Author(s):  
Yu Song Lu ◽  
Wu Sheng Wang
Keyword(s):  
Comparison Principle ◽  
Difference Equations ◽  
Upper Bound ◽  
Amplification Method ◽  
Discrete Inequalities ◽  
Change Of Variable

In this paper, two discrete inequalities with iterative summation are discussed. By technique of change of variable, comparison principle, amplification method, difference and summation, upper bound estimations of unknown functions are given. The derived results can be applied in the study of solutions of difference equations.

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