scholarly journals On the Hyers-Ulam Stability of the First-Order Difference Equation

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Soon-Mo Jung ◽  
Young Woo Nam
Keyword(s):  
Difference Equation ◽  
Ulam Stability ◽  
Order Difference ◽  
First Order ◽  
Order Difference Equation ◽  
The Difference

We prove Hyers-Ulam stability of the first-order difference equation of the formxi+1=F(i,xi), whereFis a given function with some moderate features. Moreover, we introduce some conditions for the functionFunder which the difference equation is not stable in the sense of Hyers and Ulam.

scholarly journals DIFFERENCE EQUATION OF THE COLORED JONES POLYNOMIAL FOR TORUS KNOT

2004 ◽  
Vol 15 (09) ◽  
pp. 959-965 ◽  
Author(s):  
KAZUHIRO HIKAMI
Keyword(s):  
Difference Equation ◽  
Jones Polynomial ◽  
Order Difference ◽  
Colored Jones Polynomial ◽  
First Order ◽  
Torus Knot ◽  
Second Order Difference Equation ◽  
Order Difference Equation ◽  
Hypergeometric Type ◽  
The Difference

We prove that the N-colored Jones polynomial for the torus knot [Formula: see text] satisfies the second order difference equation, which reduces to the first order difference equation for a case of [Formula: see text]. We show that the A-polynomial of the torus knot can be derived from the difference equation. Also constructed is a q-hypergeometric type expression of the colored Jones polynomial for [Formula: see text].

scholarly journals Distribution of iterates of first order difference equations

1980 ◽  
Vol 22 (1) ◽  
pp. 133-143 ◽  
Author(s):  
James B. McGuire ◽  
Colin J. Thompson
Keyword(s):  
Invariant Measure ◽  
Difference Equation ◽  
Lebesgue Measure ◽  
Difference Equations ◽  
Absolutely Continuous ◽  
Order Difference ◽  
First Order ◽  
Order Difference Equation ◽  
The Difference ◽  
Biological Context

An invariant measure which is absolutely continuous with respect to Lebesgue measure is constructed for a particular first order difference equation that has an extensive biological pedigree. In a biological context this invariant measure gives the density of the population whose growth is governed by the difference equation. Further asymptotically universal results are obtained for a class of difference equations.

AN OSCILLATION CRITERION FOR FIRST ORDER DIFFERENCE EQUATION

2020 ◽  
Vol 33 (01) ◽  
Author(s):  
Thaniyarasu Kumar ◽  
◽  
Govindasamy Ayyappan ◽  
Keyword(s):  
Difference Equation ◽  
Oscillation Criterion ◽  
Order Difference ◽  
First Order ◽  
Order Difference Equation

On the solutions of a higher order difference equation

2020 ◽  
Vol 27 (2) ◽  
pp. 165-175 ◽  
Author(s):  
Raafat Abo-Zeid
Keyword(s):  
Difference Equation ◽  
Explicit Formula ◽  
Initial Conditions ◽  
Global Behavior ◽  
Real Numbers ◽  
Positive Real ◽  
Order Difference ◽  
Forbidden Set ◽  
Order Difference Equation ◽  
The Difference

AbstractIn this paper, we determine the forbidden set, introduce an explicit formula for the solutions and discuss the global behavior of solutions of the difference equationx_{n+1}=\frac{ax_{n}x_{n-k}}{bx_{n}-cx_{n-k-1}},\quad n=0,1,\ldots,where{a,b,c}are positive real numbers and the initial conditions{x_{-k-1},x_{-k},\ldots,x_{-1},x_{0}}are real numbers. We show that when{a=b=c}, the behavior of the solutions depends on whetherkis even or odd.

Sign in / Sign up

Export Citation Format

Share Document