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Stability of First Order Linear General Quantum Difference Equations in a Banach Algebra |
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PP: 101-108 |
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doi:10.18576/amis/160110
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Author(s) |
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Enas M. Shehata,
Nashat Faried,
Rasha M. El Zafarani,
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Abstract |
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| The general quantum difference operator Dβ is defined by Dβ y(t ) = (y(β (t )) − y(t )) /(β (t ) − t ), β (t ) ̸= t where the function β(t) is strictly increasing continuous on an interval I ⊆ R and has a unique fixed point s0 ∈ I. In this paper, we establish the characterizations of stability of the first order linear β -difference equations, associated with Dβ , in a Banach algebra E with a unit e and norm ∥ · ∥. We prove the uniform stability, asymptotic stability, exponential stability and h-stability of these equations.
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