Abstract
In this paper, we are applied a new approach to prove that the solution of the linear Fredholm operator equation of the third kind given on a segment and having a finite number of multipoint singularities is equivalent to the solution of the linear Fredholm operator equation of the second kind with additional conditions. We are showed an example of solving the system of linear integral Fredholm equations of the third kind based on the equivalence of the above equations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
A. S. Apartsyn, Nonclassical Linear Volterra Equations of the First Kind (VSP, Utrecht, 2003).
A. Asanov, Regularization, Uniqueness and Existence of Solutions of Volterra Equations of the First Kind (VSP, Utrecht, 1998).
A. Asanov and R. A. Asanov, ‘‘One class of systems of linear Fredholm integral equations of the third kind of the real line with multipoint singularities,’’ Differ. Equat. 56, 1363–1370 (2020).
A. Asanov, K. B. Matanova, and R. A. Asanov, ‘‘A class of linear and nonlinear Fredholm integral equations of the third kind,’’ Kuwait J. Sci. 44, 17–28 (2017).
A. Asanov and J. Orozmamatova, ‘‘About uniqueness of solutions of Fredholm linear integral equations of the first kind in the axis,’’ Filomat 33, 1329–1333 (2019). https://doi.org/10.2298/FIL1905329A
A. L. Bukhgeim, Volterra Equations and Inverse Problems (VSP, Utrecht, 1999).
A. M. Denisov, Elements of the Theory of Inverse Problems (VSP, Utrecht, 1999).
M. I. Imanaliev and A. Asanov, ‘‘Solutions of systems of nonlinear Volterra integral equations of the first kind,’’ Dokl. Math. 40, 610–613 (1989).
M. I. Imanaliev and A. Asanov, ‘‘Regularization and uniqueness of solutions to systems of nonlinear Volterra integral equations of the third kind,’’ Dokl. Math. 76, 490–493 (2007).
M. I. Imanaliev and A. Asanov, ‘‘Solutions of system of Fredholm linear integral Equations of the third kind,’’ Dokl. Math. 81, 115–118 (2010).
M. I. Imanaliev, A. Asanov, and R. A. Asanov, ‘‘A class of systems of linear Fredholm integral equations of the third kind,’’ Dokl. Math. 83, 227–231 (2011).
T. T. Karakeev and T. M. Imanaliev, ‘‘Regularization of Volterra linear integral equations of the first kind with the smooth data,’’ Lobachevskii J. Math. 41, 39–45 (2020).
M. M. Lavrent’ev, V. G. Romanov, and S. P. Shishatskii, Ill-Posed Problems of Mathematical Physics (Am. Math. Soc., Providence, RI, 1986).
K. Yosida, Functional Analysis (Springer, Berlin, Heidelberg, New York, 1980).
ACKNOWLEDGMENTS
We are grateful to reviewers for careful reading of the manuscript and valuable comments which improve the presentation of the paper.
Author information
Authors and Affiliations
Corresponding authors
Additional information
(Submitted by T. K. Yuldashev)
Rights and permissions
About this article
Cite this article
Asanov, A., Matanova, K.B. & Asanov, R. One Class of Linear Fredholm Operator Equations of the Third Kind. Lobachevskii J Math 42, 502–507 (2021). https://doi.org/10.1134/S1995080221030057
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1995080221030057