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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.

The issue of the uniqueness of the solution for a new class of linear integral Volterra equations of the third kind on a segment is studied. On the basis of the method of integral transformations and the method of non-negative quadratic forms, uniqueness theorems for solutions are proved for a given class of integral equations of the third kind.

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