Hyers-Ulam stability of a certain Fredholm integral equation

Abstract

In this paper, by using fixed point theorem we establish the Hyers-Ulam stability and Hyers-Ulam-Rassias stability of certain homogeneous Fredholm Integral equation of the second kind $varphi (x)=lambda int_{0}^{1}(1+x+t)varphi (t)dt$ and the nonhomogeneous equation $varphi (x)=x+lambda int_{0}^{1}(1+x+t)varphi (t)dt$ for all $xin left [ 0,1 right ] and 0