On Converses to the Stability Theorems for Difference Equations

1972 ◽  
Vol 10 (1) ◽  
pp. 76-81 ◽  
Author(s):  
S. P. Gordon
Keyword(s):  
Difference Equations ◽  
Stability Theorems ◽  
The Stability

On the Necessary and Sufficient Conditions for the Stability of Linear Generalized Ordinary Differential, Linear Impulsive and Linear Difference Systems

2009 ◽  
Vol 16 (4) ◽  
pp. 597-616
Author(s):  
Shota Akhalaia ◽  
Malkhaz Ashordia ◽  
Nestan Kekelia
Keyword(s):  
Linear System ◽  
Difference Equations ◽  
Closed Interval ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Difference Systems ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Generalized Ordinary Differential Equations ◽  
Lyapunov Sense

Abstract Necessary and sufficient conditions are established for the stability in the Lyapunov sense of solutions of a linear system of generalized ordinary differential equations 𝑑𝑥(𝑡) = 𝑑𝐴(𝑡) · 𝑥(𝑡) + 𝑑𝑓(𝑡), where and are, respectively, matrix- and vector-functions with bounded total variation components on every closed interval from . The results are realized for the linear systems of impulsive, ordinary differential and difference equations.

On the Stability of Positive Difference Equations

2009 ◽  
Vol 42 (14) ◽  
pp. 156-161
Author(s):  
M. DiLoreto ◽  
J.J. Loiseau
Keyword(s):  
Difference Equations ◽  
Positive Difference ◽  
The Stability

scholarly journals A General Theorem on the Stability of a Class of Functional Equations Including Quartic-Cubic-Quadratic-Additive Equations

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 282
Author(s):  
Yang-Hi Lee ◽  
Soon-Mo Jung
Keyword(s):  
Functional Equations ◽  
Direct Method ◽  
General Theorem ◽  
Stability Problems ◽  
General Stability ◽  
Stability Theorems ◽  
Additive Type ◽  
The Stability

We prove general stability theorems for n-dimensional quartic-cubic-quadratic-additive type functional equations of the form by applying the direct method. These stability theorems can save us the trouble of proving the stability of relevant solutions repeatedly appearing in the stability problems for various functional equations.

The Stability Theorems for Subgroups of and

1994 ◽  
Vol 46 (5) ◽  
pp. 995-1006 ◽  
Author(s):  
Ali Lari-Lavassani ◽  
Yung-Chen Lu
Keyword(s):  
Large Class ◽  
Structural Stability ◽  
Singularity Theory ◽  
Stability Theorems ◽  
The Stability

AbstractIn singularity theory, J. Damon gave elegant versions of the unfolding and determinacy theorems for geometric subgroups of . and . In this work, we propose a unified treatment of the smooth stability of germs and the structural stability of versai unfoldings for a large class of such subgroups.

Stability of Weighted Darma Filters

1998 ◽  
Vol 41 (1) ◽  
pp. 49-64
Author(s):  
K. J. Harrison ◽  
J. A. Ward ◽  
L-J. Eaton
Keyword(s):  
Difference Equations ◽  
Shift Operator ◽  
Variable Coefficients ◽  
Weighted Shift ◽  
Linear Difference Equations ◽  
Linear Filters ◽  
Weighted Shift Operator ◽  
Rational Transfer ◽  
The Stability ◽  
Special Case

AbstractWe study the stability of linear filters associated with certain types of linear difference equations with variable coefficients. We show that stability is determined by the locations of the poles of a rational transfer function relative to the spectrum of an associated weighted shift operator. The known theory for filters associated with constant-coefficient difference equations is a special case.

scholarly journals Generalized Hyers–Ulam Stability of the Additive Functional Equation

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 76 ◽  
Author(s):  
Yang-Hi Lee ◽  
Gwang Kim
Keyword(s):  
Functional Equation ◽  
Additive Function ◽  
Additive Functional ◽  
Stability Theorem ◽  
Ulam Stability ◽  
Additive Functional Equation ◽  
Stability Theorems ◽  
The Stability

We will prove the generalized Hyers–Ulam stability and the hyperstability of the additive functional equation f(x1 + y1, x2 + y2, …, xn + yn) = f(x1, x2, … xn) + f(y1, y2, …, yn). By restricting the domain of a mapping f that satisfies the inequality condition used in the assumption part of the stability theorem, we partially generalize the results of the stability theorems of the additive function equations.

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