Email this article Uniqueness of the solution of one class of Volterra-Stieltjes linear integral equations of the third kind
- Authors: Asanov A.1, Matanova K.1, Absamat kyzy E.1
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Affiliations:
- Kyrgyz-Turkish Manas University
- Issue: Vol 24, No 1 (2022)
- Pages: 11-20
- Section: Mathematics
- Submitted: 15.12.2025
- Accepted: 15.12.2025
- Published: 24.02.2022
- URL: https://bakhtiniada.ru/2079-6900/article/view/358143
- DOI: https://doi.org/10.15507/2079-6900.24.202201.11-20
- ID: 358143
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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.
About the authors
Avyt Asanov
Kyrgyz-Turkish Manas University
Email: avyt.asanov@manas.edu.kg
ORCID iD: 0000-0002-0608-0860
Professor, Department of Mathematics, Kyrgyz-Turkish Manas University
Kyrgyzstan, 56 Chyngyz Aitmatov Av., Bishkek 720044, KyrgyzstanKalyskan Matanova
Kyrgyz-Turkish Manas University
Email: kalys.matanova@manas.edu.kg
ORCID iD: 0000-0002-5350-5198
Associate Professor, Department of Mathematics, Kyrgyz-Turkish Manas University
Kyrgyzstan, 56 Chyngyz Aitmatov Av., Bishkek 720044, KyrgyzstanEliza Absamat kyzy
Kyrgyz-Turkish Manas University
Author for correspondence.
Email: 2051y03002@manas.edu.kg
ORCID iD: 0000-0002-8470-7446
Master student, Graduate School of Natural And Applied Sciences, Kyrgyz-Turkish Manas University
Kyrgyzstan, 56 Chyngyz Aitmatov Av., Bishkek 720044, KyrgyzstanReferences
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