Abstract
We investigate the approximation of the solution of an integral equation in the space of continuous functions with the uniform metric by linear combinations of given functions. We also consider the approximation of the solution on arbitrary subsets of the original interval on which the integral equation is defined. We show that the sequence of minimizing generalized polynomials converges on points sets to the solution of the integral equation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
I. S. Berezin and N. P. Zhidkov, Numerical Methods [in Russian], Vol. 1, Fizmatgiz, Moscow (1959).
I. P. Ganzhela and P. P. Ganzhela, “Best approximations of integral equations,” Dokl. Akad. Nauk UkrSSR, No. 6, 492–494 (1974).
M. L. Krasnov, Integral Equations [in Russian], Nauka, Moscow (1975).
W. A. Coppel, Stability and Asymptotic Behavior of Differential Equations, vol. X, Heath, Boston (1965).
P. J. Davis, Interpolation and Approximation, Vol. XVI, Blaisdell Publ. Co., New York (1963).
Author information
Authors and Affiliations
Additional information
Translated from Vychislitel'naya i Prikladnaya Matematika, No. 59, pp. 16–24, 1986.
Rights and permissions
About this article
Cite this article
Ganzhela, I.F. Convergence of generalized polynomials to the solution of an integral equation. J Math Sci 60, 1442–1449 (1992). https://doi.org/10.1007/BF01095737
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01095737