Existence of ψψ-bounded solutions for linear difference equations

In this work we define ΨΨ-boundedness of sequences and discuss the existence of ΨΨ-bounded solutions for linear difference equations. We present a necessary and sufficient condition for the existence of ΨΨ-bounded solutions for the linear nonhomogeneous difference equation x(n+1)=A(n)x(n)+f(n)x(n+1)=A(n)x(n)+f(n).