On Ulam stability of a third order linear difference equation in Banach spaces

2020 ◽  
Vol 94 (6) ◽  
pp. 1151-1170 ◽  
Author(s):  
Alina Ramona Baias ◽  
Dorian Popa
Keyword(s):  
Difference Equation ◽  
Banach Spaces ◽  
Linear Difference Equation ◽  
Ulam Stability ◽  
Third Order ◽  
Order Linear

scholarly journals Instability of second-order nonhomogeneous linear difference equations with real-valued coefficients

2021 ◽  
Vol 37 (3) ◽  
pp. 489-495
Author(s):  
MASAKAZU ONITSUKA ◽  
◽  
Keyword(s):  
Difference Equation ◽  
Linear Difference Equation ◽  
Second Order ◽  
Ulam Stability ◽  
Necessary And Sufficient Condition ◽  
Linear Difference Equations ◽  
Real Numbers ◽  
Step Size ◽  
Order Linear ◽  
Necessary And Sufficient

In J. Comput. Anal. Appl. (2020), pp. 152--165, the author dealt with Hyers--Ulam stability of the second-order linear difference equation $\Delta_h^2x(t)+\alpha \Delta_hx(t)+\beta x(t) = f(t)$ on $h\mathbb{Z}$, where $\Delta_hx(t) = (x(t+h)-x(t))/h$ and $h\mathbb{Z} = \{hk|\,k\in\mathbb{Z}\}$ for the step size $h>0$; $\alpha$ and $\beta$ are real numbers; $f(t)$ is a real-valued function on $h\mathbb{Z}$. The purpose of this paper is to clarify that the second-order linear difference equation has no Hyers--Ulam stability when the step size $h>0$ and the coefficients $\alpha$ and $\beta$ satisfy suitable conditions. Finally, a necessary and sufficient condition for Hyers--Ulam stability is obtained.

Best Ulam constant for a linear difference equation

2019 ◽  
Vol 35 (1) ◽  
pp. 13-22 ◽  
Author(s):  
ALINA-RAMONA BAIAS ◽  
◽  
FLORINA BLAGA ◽  
DORIAN POPA ◽  
◽  
...  
Keyword(s):  
Difference Equation ◽  
Banach Spaces ◽  
Linear Difference Equation ◽  
Ulam Stability

In this paper we provide some results on Ulam stability for the linear difference equation of order one in Banach spaces and we determine its best Ulam constant. The main result is applied to a process of loan amortization.

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