Regularization and Choice of the Parameter for the Third Kind Nonlinear Volterra-Stieltjes Integral Equation Solutions

Abstract

The article is considering the third kind of nonlinear Volterra-Stieltjes integral equations with the solution by Lavrentyev regularizing operator. A uniqueness theorem was proved, and a regularization parameter was chosen. This can be used in further development of the theory of the integral equations in non-standard problems, classes in the numerical solution of third kind Volterra-Stieltjes integral equations, and when solving specific problems that lead to equations of the third kind.

Uniqueness of the Fredholm-Stiltjes Linear Integral Equations Solutions of the Third Kind

“…In [4], a theory is presented and numerical methods are used for solving non-to an increasing function was introduced, using linear Fredholm-Stiltjes integral equations of the first kind in [16] [17] [18]. Numerical solution of the Fredholm and Volterra Integral equations by using modified Bernstein-Kantorovich operators [19], second kind [20], and third kind of nonlinear Volterra-Stieltjes integral equations with the solution by Lavrentyev regularizing operator were also described [21].…”