Kadenova Z.A.   Asanov A.  

Regularization and uniqueness of solutions of systems Fredholm-Stieltjes linear integral equations of the first kind with two variables

Reporter: Kadenova Z.A.

REGULARIZATION AND UNIQUENESS OF SOLUTIONS OF SYSTEMS FREDHOLM-STIELTJES LINEAR INTEGRAL EQUATIONS OF THE FIRST KIND WITH TWO VARIABLES

A. Asanov, Z. A.Kadenova
Bishkek, Kyrgyzstan,
avyt.asanov@manas.edu.kg, kadenova71@mail.ru

     Various issues concerning of integral equations of the first kind were studied in [1-6]. Some practical and theoretical investigations were made in paper [1] for nonclassical Volterra integral equations of the first kind. In [2] for system of Volterra integral equations of  the first kind were  constructed  the Volterra regularized operators. In [3] the paper a theorem is proved the uniqueness of the solution of Fredholm-Stielties integral equations of the  rst kind with two independent variables. In  [4] for the systems of Volterra integral  equations of the first kind with two independent  variables were investigated the problems of regularization  and uniqueness.  More specifically, fundamental results for Fredholm integral equations of the first kind were obtained in [5], where regularizing operators in the sense of M.M.Lavrent’ev vere constructed for solutions of  linear Fredholm integral equations of the first kind.
In this work for the investigation of the integral equation  we it is based on the notion of the derivative of function with respect to the strictly increasing function [7]. Apparently the first notion of  the derivative, with respect to the strictly increasing function, was introduced in [7].

References
1. A.S. Aparstyn, Nonclassical linear Volterra Equations of  the First Kind. VSP, Utrecht, p.168, (2003).
2. A.Asanov, Regularization, Uniqueness and Existence of Solutions of Volterra Equations of  the First Kind. VSP, Utrecht, p.272. (1998).
3.  A.Asanov, Z.A. Kadenova, Uniqueness of solutions for one class of Fredholm – Stieltjes equations of the first kind with tho variables// Материалы международной научной конференции «Современные проблемы математики и механики», посвященной 80-летию академика В.А. Садовничего», МГУ имени М.В.Ломоносова, Москва, 13 - 15 мая 2019 г.- М.:МГУ, 2019.  С.177-179.
4. M.Imanaliev and  A.Asanov,  On solutions of systems of nonlinear  two-dimentional Volterra integral equations of the first kind, Dokl. Akad. Nauk  SSSR, 317(1), (1991).
5. M.M.Lavrentiev, On-integral equations of  the first kind, Dokl. Akad. Nauk SSSR, 127(1), 31-33, (1959).
6. M.IImanaliev, A.Asanov and  Z.A.Kadenova,  A Class of linear integral equations of  the first kind with two independent variables, Doklady Mathematucs , 89(1), 98-102 (2014).
7. A.Asanov, The derivative of a function by means of a increasing function, Fen Bilimleri Dergisi, Kyrgyz-Turkish Manas University, 1, 18-64 (2001).   

Abstracts file: KadenovaZA.zip


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