scholarly journals A Class of Volterra-Fredholm Type Weakly Singular Difference Inequalities with Power Functions and Their Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Yange Huang ◽  
Wu-Sheng Wang ◽  
Yong Huang
Keyword(s):  
Difference Equations ◽  
Upper Bounds ◽  
Power Functions ◽  
Fredholm Type ◽  
Analysis Techniques ◽  
Weakly Singular

We discuss a class of Volterra-Fredholm type difference inequalities with weakly singular. The upper bounds of the embedded unknown functions are estimated explicitly by analysis techniques. An application of the obtained inequalities to the estimation of Volterra-Fredholm type difference equations is given.

scholarly journals Generalized Nonlinear Volterra-Fredholm Type Integral Inequality with Two Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Yusong Lu ◽  
Wu-Sheng Wang ◽  
Xiaoliang Zhou ◽  
Yong Huang
Keyword(s):  
Differential Equations ◽  
Integral Inequality ◽  
Inverse Function ◽  
Upper Bounds ◽  
Fredholm Type ◽  
Analysis Techniques ◽  
Amplification Method ◽  
Type Integral ◽  
Dialectical Relationship ◽  
Change Of Variable

We establish a class of new nonlinear retarded Volterra-Fredholm type integral inequalities, with two variables, where known functionwin integral functions in Q.-H. Ma and J. Pečarić, 2008 is changed into the functionsw1,w2. By adopting novel analysis techniques, such as change of variable, amplification method, differential and integration, inverse function, and the dialectical relationship between constants and variables, the upper bounds of the embedded unknown functions are estimated. The derived results can be applied in the study of solutions of ordinary differential equations and integral equations.

scholarly journals Event-Triggering State and Fault Estimation for a Class of Nonlinear Systems Subject to Sensor Saturations

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1242
Author(s):  
Cong Huang ◽  
Bo Shen ◽  
Lei Zou ◽  
Yuxuan Shen
Keyword(s):  
Nonlinear Systems ◽  
Difference Equations ◽  
Estimation Error ◽  
Upper Bounds ◽  
The State ◽  
Fault Estimation ◽  
Triggering Mechanism ◽  
Transmission Frequency ◽  
Current Transmission ◽  
Event Triggering

This paper is concerned with the state and fault estimation issue for nonlinear systems with sensor saturations and fault signals. For the sake of avoiding the communication burden, an event-triggering protocol is utilized to govern the transmission frequency of the measurements from the sensor to its corresponding recursive estimator. Under the event-triggering mechanism (ETM), the current transmission is released only when the relative error of measurements is bigger than a prescribed threshold. The objective of this paper is to design an event-triggering recursive state and fault estimator such that the estimation error covariances for the state and fault are both guaranteed with upper bounds and subsequently derive the gain matrices minimizing such upper bounds, relying on the solutions to a set of difference equations. Finally, two experimental examples are given to validate the effectiveness of the designed algorithm.

scholarly journals Two periodic solutions of neutral difference equations modelling physiological processes

2006 ◽  
Vol 2006 ◽  
pp. 1-12 ◽  
Author(s):  
Jun Wu ◽  
Yicheng Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Difference Equations ◽  
Neutral Difference Equations ◽  
First Order ◽  
Analysis Techniques ◽  
Physiological Processes

We establish existence, multiplicity, and nonexistence of periodic solutions for a class of first-order neutral difference equations modelling physiological processes and conditions. Our approach is based on a fixed point theorem in cones as well as some analysis techniques.

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 A Nonlinear Weakly Singular Retarded Henry-Gronwall Type Integral Inequality and Its Application

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yuanhua Lin ◽  
Shanhe Wu ◽  
Wu-Sheng Wang
Keyword(s):  
Differential Equations ◽  
Singular Integral ◽  
Fractional Differential Equations ◽  
Integral Inequality ◽  
Analysis Techniques ◽  
Weakly Singular ◽  
Type Integral ◽  
Explicit Bounds ◽  
Fractional Differential ◽  
Equations With Delay

We establish a class of new nonlinear retarded weakly singular integral inequality. Under several practical assumptions, the inequality is solved by adopting novel analysis techniques, and explicit bounds for the unknown functions are given clearly. An application of our result to the fractional differential equations with delay is shown at the end of the paper.

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 A Generalized Nonlinear Volterra-Fredholm Type Integral Inequality and Its Application

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Limian Zhao ◽  
Shanhe Wu ◽  
Wu-Sheng Wang
Keyword(s):  
Integral Equations ◽  
Integral Inequality ◽  
Upper Bounds ◽  
Fredholm Integral Equations ◽  
Fredholm Type ◽  
Type Integral

We establish a new nonlinear retarded Volterra-Fredholm type integral inequality. The upper bounds of the embedded unknown functions are estimated explicitly by using the theory of inequality and analytic techniques. Moreover, an application of our result to the retarded Volterra-Fredholm integral equations for estimation is given.

scholarly journals Some New Nonlinear Weakly Singular Inequalities and Applications to Volterra-Type Difference Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Kelong Zheng ◽  
Wenqiang Feng ◽  
Chunxiang Guo
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Upper Bound ◽  
Singular Kernel ◽  
Nonlinear Difference Equation ◽  
Volterra Type ◽  
Weakly Singular Kernel ◽  
Weakly Singular

Some new nonlinear weakly singular difference inequalities are discussed, which generalize some known weakly singular inequalities and can be used in the analysis of nonlinear Volterra-type difference equations with weakly singular kernel. An application to the upper bound of solutions of a nonlinear difference equation is also presented.

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