In this paper, we study the existence of solutions of some nonlinear Volterra integral equations by using the techniques of measures of noncompactness and the Petryshyn's fixed point theorem in Banach space. We also present some examples of the integral equation to confirm the efficiency of our results.

One of the numerical methods for solving linear Volterra integral equations is block-by-block method, which is explained in [L.M. Delves, J.L. Mohamed, Computational Methods for Integral Equations, Cambridge University Press, 1985; L.M. Delves, J. Walsh, Numerical Solution of Integral Equations, Oxford University Press, 1974] and [P.K. Kyte, P. Puri, Computational Methods for Linear Integral Eq...

In this paper we are going to study the Hyers{Ulam{Rassias typesof stability for nonlinear, nonhomogeneous Volterra integral equations with delayon nite intervals.

Keywords: Integro-differential equations Volterra equations Abel's integral equations Bernstein polynomials Singular volterra integral equations a b s t r a c t In this study, a new collocation method based on the Bernstein polynomials is introduced for the approximate solution of a class of linear Volterra integro-differential equations with weakly singular kernel. If the exact solution is pol...

‎In this paper‎, ‎we establish the Hyers--Ulam--Rassias stability and the Hyers--Ulam stability of impulsive Volterra integral equation by using a fixed point method‎.

in this paper we consider a nonlinear two-phase stefan problem in one-dimensional space. the problem is mapped into a nonlinear volterra integral equation for the free boundary.