Stationary Hyers-Ulam-Rassias stability for a class of nonlinear Volterra integral equations

Ulam stability for a delay differential equation

“…Very important contributions to this subject were brought by Ulam [15], Rassias [10], Hyers et al [4], Jung [5], Guo et al [3], Kolmanovskiȋ and Myshkis [6], and Radu [9]. Our results are connected to some recent papers of Castro and Ramos [2] and Jung [5] (where integral and differential equations are considered), Bota-Boriceanu and Petrușel [1], and Petru et al [8] (where the Ulam-Hyers stability for operatorial equations and inclusions is discussed). Following [7,13], in present paper we will investigate Ulam-Hyers stability and generalized Ulam-Hyers-Rassias stability for the following differential equation with modification of the argument:…”

Stability of a nonlinear Volterra integro-differential equation via a fixed point approach

“…In the past recent years, several authors proved the Hyers-Ulam stability of Volterra equations of other type (we refer to [1,3,4,6,7,12]). Definition 1.1.…”

Collocation Methods for Volterra Integral and Integro-Differential Equations: A Review

“…The review of the numerical methods of optimal accuracy (spline-collocation technique) for multidimensional weakly singular VIEs is given in [57]. Some other interesting papers regard the distance between the approximate and exact solutions of various generalizations of the Volterra equations [58][59][60][61][62][63]. Lastly, we underline that in the practical applications of VIE based models it is extremely important to have the numerical method to be stable with respect to the measurement errors both in the source function and in the kernel.…”