Hyers–Ulam Stability for a First-Order Linear Proportional Nabla Difference Operator

2019 ◽  
pp. 255-272
Author(s):  
Douglas R. Anderson
Keyword(s):  
Difference Operator ◽  
Ulam Stability ◽  
Order Linear ◽  
First Order

scholarly journals HYERS-ULAM STABILITY OF FIRST ORDER LINEAR DIFFERENCE OPERATORS ON BANACH SPACE

2018 ◽  
Vol 14 (1) ◽  
pp. 7475-7485
Author(s):  
Arun Kumar Tripathy ◽  
Pragnya Senapati
Keyword(s):  
Banach Space ◽  
Difference Operator ◽  
Difference Operators ◽  
Ulam Stability ◽  
Order Linear ◽  
First Order ◽  
Linear Difference Operator

In this work, the Hyers-Ulam stability of first order linear difference operator TP defined by (Tpu)(n) = ∆u(n) - p(n)u(n); is studied on the Banach space X = l∞, where p(n) is a sequence of reals.

scholarly journals Hyers-Ulam Stability of a System of First Order Linear Recurrences with Constant Coefficients

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Bing Xu ◽  
Janusz Brzdęk
Keyword(s):  
Ulam Stability ◽  
Linear Difference Equations ◽  
Positive Real ◽  
Fixed Sequence ◽  
Linear Recurrences ◽  
Order Linear ◽  
First Order ◽  
Constant Coefficients ◽  
Complex Coefficients ◽  
Positive Real Constant

We study the Hyers-Ulam stability in a Banach spaceXof the system of first order linear difference equations of the formxn+1=Axn+dnforn∈N0(nonnegative integers), whereAis a givenr×rmatrix with real or complex coefficients, respectively, and(dn)n∈N0is a fixed sequence inXr. That is, we investigate the sequences(yn)n∈N0inXrsuch thatδ∶=supn∈N0yn+1-Ayn-dn<∞(with the maximum norm inXr) and show that, in the case where all the eigenvalues ofAare not of modulus 1, there is a positive real constantc(dependent only onA) such that, for each such a sequence(yn)n∈N0, there is a solution(xn)n∈N0of the system withsupn∈N0yn-xn≤cδ.

scholarly journals Hyers-Ulam Stability of the First-Order Matrix Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Soon-Mo Jung
Keyword(s):  
Differential Equations ◽  
Variable Coefficients ◽  
Linear Differential Equations ◽  
Ulam Stability ◽  
Order Linear ◽  
First Order ◽  
Matrix Differential Equations ◽  
Homogeneous Matrix ◽  
Linear Differential ◽  
Matrix Differential

We prove the generalized Hyers-Ulam stability of the first-order linear homogeneous matrix differential equationsy→'(t)=A(t)y→(t). Moreover, we apply this result to prove the generalized Hyers-Ulam stability of thenth order linear differential equations with variable coefficients.

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