ISSN 2079-6900 (Print)
ISSN 2587-7496 (Online)

#### Middle Volga Mathematical Society Journal

DOI 10.15507/2079-6900.24.202201.11-20

Original article

ISSN 2079-6900 (Print)

ISSN 2587-7496 (Online)

MSC2020 45A05

#### Uniqueness of the solution of one class of Volterra-Stieltjes linear integral equations of the third kind

A. Asanov, K. Matanova, E. Absamat kyzy

Kyrgyz-Turkish Manas University

Abstract. In this paper, the question of uniqueness of the solution for one class of Volterra-Stieltjes linear integral equations of the third kind is investigated. The notion of derivative with respect to an increasing function was introduced by A. Asanov in 2001 and plays special role in the study. This notion is a generalization of the usual concept of a derivative function and is an inverse operator for one class of the Stieltjes integral. Basing on idea of such derivative, using the method of integral transformations and the method of non-negative quadratic forms, the uniqueness theorems for the solution of the considered class of integral equations are proved. Examples satisfying the conditions of uniqueness theorems are also constructed in the paper. It becomes clear from these examples that it is difficult to study Volterra-Stieltjes linear integral equations of the first and third kind without using the notion of derivative with respect to increasing function.

Key Words: Volterra-Stieltjes integral equations, third kind, derivative with respect to an increasing function, uniqueness of solution

For citation: A. Asanov, K. Matanova, E. Absamat kyzy. Uniqueness of the solution of one class of Volterra-Stieltjes linear integral equations of the third kind. Zhurnal Srednevolzhskogo matematicheskogo obshchestva. 24:1(2022), 11–20. DOI: https://doi.org/10.15507/2079-6900.24.202201.11-20

Submitted: 05.12.2021; Revised: 14.02.2022; Accepted: 24.02.2022