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 Discrete Gronwall-Bellman Type Inequalities with Three Independent Variables and Applications

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Weihua Liu ◽  
Haisong Huang
Keyword(s):  
Difference Equation ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Initial Boundary ◽  
Qualitative And Quantitative ◽  
Independent Variables ◽  
Quantitative Properties

Some new discrete Gronwall-Bellman type inequalities with three independent variables which generalize some existing results and can be used as handy tools in the study of qualitative and quantitative properties of solutions of certain classes of difference equation are presented. As applications, some difference equations with the initial boundary conditions are also considered.

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.

scholarly journals Inequalities applicable in the theory of partial finite difference equations

2001 ◽  
Vol 32 (2) ◽  
pp. 155-166
Author(s):  
B. G. Pachpatte
Keyword(s):  
Finite Difference ◽  
Difference Equations ◽  
Independent Variables ◽  
Finite Difference Equations ◽  
Two Independent Variables

The main objective of this paper is to establish some new finite difference inequalities in two independent variables which can be used as handy tools in the theory of certain classes of partial finite difference equations. The analysis used in the proofs is elementary and the results established provide new estimates for these types of inequalities.

scholarly journals On nonlinear finite difference inequalities in two independent variables

2002 ◽  
Vol 33 (1) ◽  
pp. 57-66
Author(s):  
B. G. Pachpatte
Keyword(s):  
Finite Difference ◽  
Difference Equations ◽  
Qualitative Theory ◽  
Independent Variables ◽  
Finite Difference Equations ◽  
Explicit Bounds ◽  
Two Independent Variables

The aim of the present paper is to establish some new finite difference inequalities involving functions of two independent variables which provide explicit bounds on unknown functions. The inequalities given here can be used as tools in the qualitative theory of certain partial finite difference equations.

Comparing the Characteristics of Text-Speak Used by English and Japanese Students

2011 ◽  
Vol 1 (2) ◽  
pp. 45-57 ◽  
Author(s):  
Jean Underwood ◽  
Taiichiro Okubayashi
Keyword(s):  
Gender Differences ◽  
Text Messaging ◽  
Quantitative Difference ◽  
Communication Style ◽  
Japanese Students ◽  
Qualitative And Quantitative ◽  
Independent Variables ◽  
And Gender ◽  
Technological Constraints ◽  
Two Independent Variables

Text messaging is pervasive among the youth of many cultures, but the extent and nature of text-speak, the modified host language, is open to question. This study of English and Japanese undergraduates specifically investigated whether text-speak is a product of the technological constraints on the host language or is influenced by gender differences in communication style. The study had a between-subjects factorial design with two independent variables: language (English, Japanese) and gender (male, female). The dependent variable was frequency and type of text modification. The results show both a qualitative and quantitative difference in texting between the two groups with English texters being more active. However, English and Japanese females made more adaptations to the host-language than their within-culture male peers, even though the structure of the two host languages was very different. The greater use of abbreviations by females compared to males might be explained either by a higher engagement with this mode of communication or diverging goals between the sexes when texting.

scholarly journals Bounds of Double Integral Dynamic Inequalities in Two Independent Variables on Time Scales

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
S. H. Saker
Keyword(s):  
Time Scales ◽  
Unknown Function ◽  
The Other ◽  
Dynamic Equations ◽  
Double Integral ◽  
Independent Variables ◽  
Explicit Bounds ◽  
Quantitative Properties ◽  
The One ◽  
Two Independent Variables

Our aim in this paper is to establish some explicit bounds of the unknown function in a certain class of nonlinear dynamic inequalities in two independent variables on time scales which are unbounded above. These on the one hand generalize and on the other hand furnish a handy tool for the study of qualitative as well as quantitative properties of solutions of partial dynamic equations on time scales. Some examples are considered to demonstrate the applications of the results.

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.

Sign in / Sign up

Export Citation Format

Share Document