TY - JOUR
T1 - Stability of Fredholm Integral Equation of the First Kind in Reproducing Kernel Space
AU - Du , Hong
AU - Mu , Lihua
JO - Communications in Mathematical Research 
VL - 2
SP - 121
EP - 126
PY - 2021
DA - 2021/05
SN - 28
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cmr/19051.html
KW - Freholm integral equation, ill-posed problem, reproducing kernel space.
AB - <p style="text-align: justify;">It is well known that the problem on the stability of the solutions for
Fredholm integral equation of the first kind is an ill-posed problem in $C[a, b]$ or $L^2
[a, b]$.
In this paper, the representation of the solution for Fredholm integral equation of the
first kind is given if it has a unique solution. The stability of the solution is proved
in the reproducing kernel space, namely, the measurement errors of the experimental
data cannot result in unbounded errors of the true solution. The computation of
approximate solution is also stable with respect to $‖·‖_C$ or $‖·&nbsp;‖_{L^2}$. A numerical
experiment shows that the method given in this paper is stable in the reproducing
kernel space.</p>