An approximate solution for Volterra integral equations of the second kind in space with weight function

Abstract

The main aim of this study is to present a new and simple algorithm to prove that the function ϕ n (x) is a good approximation to the solution ϕ(x) for Volterra integral equations (VIEs) of the second kind in the space L 2 p(x) [0, 2π] with weight function p(x). This approximation is discussed in details with help of the Jackson's and Dirichlet's operators. Special attention is given to study the convergence analysis and estimation of an upper bound for the error of the approximated solution.Mathematics Subject Classification: 45D05, 65R20