Hyers–Ulam stability of non-autonomous and nonsingular delay difference equations

In this paper, we study the uniqueness and existence of the solution of a non-autonomous and nonsingular delay difference equation using the well-known principle of contraction from fixed point theory. Furthermore, we study the Hyers–Ulam stability of the given system on a bounded discrete interval...

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Bibliographic Details
Published in:Advances in difference equations Vol. 2021; no. 1; pp. 1 - 15
Main Authors: Rahmat, Gul, Ullah, Atta, Rahman, Aziz Ur, Sarwar, Muhammad, Abdeljawad, Thabet, Mukheimer, Aiman
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 26.10.2021
Springer Nature B.V
SpringerOpen
Subjects:
Analysis
Control theory
Difference and Functional Equations
Difference Equations
Fixed points (mathematics)
Functional Analysis
Hyer–Ulam
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Special Functions and Orthogonal Polynomials
Stability
35R11
Stability
Difference equations
Hyer–Ulam
34A08
ISSN:1687-1847, 1687-1839, 1687-1847
Online Access:Get full text
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Summary:In this paper, we study the uniqueness and existence of the solution of a non-autonomous and nonsingular delay difference equation using the well-known principle of contraction from fixed point theory. Furthermore, we study the Hyers–Ulam stability of the given system on a bounded discrete interval and then on an unbounded interval. An example is also given at the end to illustrate the theoretical work.
Bibliography:ObjectType-Article-1
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ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-021-03627-y