Existence of Ψ-Bounded Solutions for Linear Matrix Difference Equations on Z+

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DOI:

https://doi.org/10.4067/S0719-06462014000100004

Abstract

This paper deals with obtaining necessary and sufficient conditions for the existence of at least one Ψ-bounded solution for the linear matrix difference equation X(n + 1) = A(n)X(n)B(n) + F(n), where F(n) is a Ψ-summable matrix valued function on Z+. Finally, we prove a result relating to the asymptotic behavior of the Ψ-bounded solutions of this equation on Z+.

Keywords

Difference Equations , Fundamental Matrix , Ψ-bounded , Ψ-summable , Kronecker product
  • G. Suresh Koneru Lakshmaiah University, Department of Mathematics, Vaddeswaram, Guntur dt., A.P., India.
  • Ch Vasavi Koneru Lakshmaiah University, Department of Mathematics, Vaddeswaram, Guntur dt., A.P., India.
  • T.S. Rao Koneru Lakshmaiah University, Department of Mathematics, Vaddeswaram, Guntur dt., A.P., India.
  • M.S.N. Murty Acharya Nagarjuna University, Department of Mathematics, Nagarjuna Nagar-522510, Guntur dt., A.P., India.
  • Pages: 37–48
  • Date Published: 2014-03-01
  • Vol. 16 No. 1 (2014): CUBO, A Mathematical Journal

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Published

2014-03-01

How to Cite

[1]
G. Suresh, C. Vasavi, T. Rao, and M. Murty, “Existence of Ψ-Bounded Solutions for Linear Matrix Difference Equations on Z+”, CUBO, vol. 16, no. 1, pp. 37–48, Mar. 2014.

Issue

Vol. 16 No. 1 (2014): CUBO, A Mathematical Journal

Section

Articles