h-STABILITY OF PERTURBED VOLTERRA DIFFERENCE SYSTEMS

Bounded Solutions of Perturbed Volterra lntegrodifferential Systems

More recently (P) has been studied under the weaker assumption that (L) is admissible with respect to certain pairs of spaces. The author [2] proved under such admissibility assumptions that locally the set of bounded solutions of (P) is homeomorphic to the set of bounded solutions of (L), provided p satisfies a Lipschitz-type condition in X. Other authors [I, 6J have obtained similar and relat...

Stability of nonlinear h-difference systems with n fractional orders

Stability and Asymptoticity of Volterra Difference Equations: A Progress Report

We survey some of the fundamental results on the stability and asymptoticity of linear Volterra difference equations. The method of Z-transform is heavily utilized in equations of convolution type. An example is given to show that uniform asymptotic stability does not necessarily imply exponential stabilty. It is shown that the two notions are equivalent if the kernel decays exponentially. For ...

h-Stability for Differential Systems Relative to Initial Time Difference

and Applied Analysis 3 Moreover, using the condition (iii), we obtain z (t) ≤ h (t) h −1 (τ 0 ) ( 󵄩󵄩󵄩󵄩y0 − x0 󵄩󵄩󵄩󵄩 + 󵄨󵄨󵄨󵄨η 󵄨󵄨󵄨󵄨) . (12) Then from (12), we get 󵄩󵄩󵄩󵄩x (t, τ0, y0) − x (t − η, t0, x0) 󵄩󵄩󵄩󵄩 ≤ [ 󵄩󵄩󵄩󵄩y0 − x0 󵄩󵄩󵄩󵄩 + 󵄨󵄨󵄨󵄨τ0 − t0 󵄨󵄨󵄨󵄨] h (t) h −1 (τ 0 ) . (13) So by Definition 1 with c = 1, the solution x(t, τ 0 , y 0 ) of (2) is ITDhS with respect to the solution x(t − η, t 0 , x 0 ). T...

Fuzzy difference equations of Volterra type

In this work we introduce the notion of fuzzy volterra dierence equations and study the dynamicalproperties of some classes of this type of equations. We prove some comparison theorems for theseequations in terms of ordinary volterra dierence equations. Using these results the stability of thefuzzy nonlinear volterra dierence equations is investigated.