Stability of First Order Linear General Quantum Difference Equations in a Banach Algebra

Authors

Enas M. Shehata, Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shibin El-Kom 32511, EgyptFollow
Nashat Faried, Department of Mathematics, Faculty of Science, Ain Shams University, Cairo, EgyptFollow
Rasha M. El Zafarani, Department of Mathematics, Faculty of Science, Ain Shams University, Cairo, EgyptFollow

Author Country (or Countries)

Egypt

Abstract

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.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/160110

Recommended Citation

M. Shehata, Enas; Faried, Nashat; and M. El Zafarani, Rasha (2022) "Stability of First Order Linear General Quantum Difference Equations in a Banach Algebra," Applied Mathematics & Information Sciences: Vol. 16: Iss. 1, Article 10.
DOI: http://dx.doi.org/10.18576/amis/160110
Available at: https://digitalcommons.aaru.edu.jo/amis/vol16/iss1/10