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

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 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.

Mixing for stationary processes with finite-order multiple Wiener-Itô integral representation

1996 ◽  
Vol 16 (5) ◽  
pp. 1087-1100
Author(s):  
Eric Slud ◽  
Daniel Chambers
Keyword(s):  
Large Class ◽  
Order Term ◽  
Sufficient Conditions ◽  
Polynomial Form ◽  
Itô Integral ◽  
Ito Integral ◽  
Weakly Mixing ◽  
Subordinated Processes ◽  
Infinite Sums ◽  
Necessary And Sufficient

abstractNecessary and sufficient analytical conditions are given for homogeneous multiple Wiener-Itô integral processes (MWIs) to be mixing, and sufficient conditions are given for mixing of general square-integrable Gaussian-subordinated processes. It is shown that every finite or infinite sum Y of MWIs (i.e. every real square-integrable stationary polynomial form in the variables of an underlying weakly mixing Gaussian process) is mixing if the process defined separately by each homogeneous-order term is mixing, and that this condition is necessary for a large class of Gaussian-subordinated processes. Moreover, for homogeneous MWIs Y1, for sums of MWIs of order ≤ 3, and for a large class of square-integrable infinite sums Y1, of MWIs, mixing holds if and only if Y2 has correlation-function decaying to zero for large lags. Several examples of the criteria for mixing are given, including a second-order homogeneous MWI, i.e. a degree two polynomial form, orthogonal to all linear forms, which has auto-correlations tending to zero for large lags but is not mixing.

On a nonlinear integro-differential equation of Fredholm type

2021 ◽  
Vol 13 (2) ◽  
pp. 194
Author(s):  
Mohammed Charif Bounaya ◽  
Samir Lemita ◽  
Mourad Ghiat ◽  
Mohamed Zine Aissaoui
Keyword(s):  
Differential Equation ◽  
Fredholm Type ◽  
Integro Differential Equation
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