Geodesic
Uniqueness of the solution of one class of Volterra-Stieltjes linear integral equations of the third kind
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 24 (2022) no. 1, pp. 11-20

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Mots-clés : Volterra-Stieltjes integral equations
Keywords: third kind, derivative with respect to an increasing function, uniqueness of solution. 
@article{SVMO_2022_24_1_a0,
     author = {A. Asanov and K. Matanova and E. Absamat kyzy},
     title = {Uniqueness of the solution of one class of {Volterra-Stieltjes} linear integral equations of the third kind},
     journal = {\v{Z}urnal Srednevol\v{z}skogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {11--20},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVMO_2022_24_1_a0/}
}
TY  - JOUR
AU  - A. Asanov
AU  - K. Matanova
AU  - E. Absamat kyzy
TI  - Uniqueness of the solution of one class of Volterra-Stieltjes linear integral equations of the third kind
JO  - Žurnal Srednevolžskogo matematičeskogo obŝestva
PY  - 2022
SP  - 11
EP  - 20
VL  - 24
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SVMO_2022_24_1_a0/
LA  - ru
ID  - SVMO_2022_24_1_a0
ER  - 
%0 Journal Article
%A A. Asanov
%A K. Matanova
%A E. Absamat kyzy
%T Uniqueness of the solution of one class of Volterra-Stieltjes linear integral equations of the third kind
%J Žurnal Srednevolžskogo matematičeskogo obŝestva
%D 2022
%P 11-20
%V 24
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SVMO_2022_24_1_a0/
%G ru
%F SVMO_2022_24_1_a0
A. Asanov; K. Matanova; E. Absamat kyzy. Uniqueness of the solution of one class of Volterra-Stieltjes linear integral equations of the third kind. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 24 (2022) no. 1, pp. 11-20. http://geodesic.mathdoc.fr/item/SVMO_2022_24_1_a0/