First-Order Linear Dynamic Equations

2020 ◽  
pp. 61-91
Author(s):  
Douglas R. Anderson ◽  
Svetlin G. Georgiev
Keyword(s):  
Dynamic Equations ◽  
Order Linear ◽  
First Order ◽  
Linear Dynamic

scholarly journals Hyers-Ulam and Hyers-Ulam-Rassias stability of first-order linear dynamic equations

2021 ◽  
Vol 109 (123) ◽  
pp. 83-93
Author(s):  
Maryam Alghamdi ◽  
Alaa Aljehani ◽  
Martin Bohner ◽  
Alaa Hamza
Keyword(s):  
Banach Space ◽  
Time Scale ◽  
Sufficient Conditions ◽  
Dynamic Equations ◽  
Order Linear ◽  
First Order ◽  
Linear Dynamic ◽  
Rassias Stability

We present several new sufficient conditions for Hyers-Ulam and Hyers-Ulam-Rassias stability of first-order linear dynamic equations for functions defined on a time scale with values in a Banach space.

scholarly journals Hyers-Ulam stability of first-order homogeneous linear dynamic equations on time scales

2018 ◽  
Vol 51 (1) ◽  
pp. 198-210 ◽  
Author(s):  
Douglas R. Anderson ◽  
Masakazu Onitsuka
Keyword(s):  
Time Scales ◽  
Dynamic Equations ◽  
Ulam Stability ◽  
Step Size ◽  
First Order ◽  
Linear Dynamic ◽  
Discrete Step ◽  
Special Cases ◽  
Parameter Values ◽  
Homogeneous Linear

Abstract We establish theHyers-Ulam stability (HUS) of certain first-order linear constant coefficient dynamic equations on time scales, which include the continuous (step size zero) and the discrete (step size constant and nonzero) dynamic equations as important special cases. In particular, for certain parameter values in relation to the graininess of the time scale, we find the minimum HUS constants. A few nontrivial examples are provided. Moreover, an application to a perturbed linear dynamic equation is also included.

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