Opuscula Math. 36, no. 4 (2016), 459-470
http://dx.doi.org/10.7494/OpMath.2016.36.4.459
Opuscula Mathematica
Some stability conditions for scalar Volterra difference equations
Leonid Berezansky
Małgorzata Migda
Ewa Schmeidel
Abstract. New explicit stability results are obtained for the following scalar linear difference equation \[x(n+1)-x(n)=-a(n)x(n)+\sum_{k=1}^n A(n,k)x(k)+f(n)\] and for some nonlinear Volterra difference equations.
Keywords: linear and nonlinear Volterra difference equations, boundedness of solutions, exponential and asymptotic stability.
Mathematics Subject Classification: 34A10, 39A22, 39A30.