Hyers-Ulam stability of a certain Fredholm integral equation

Authors: ALBERTO SIMÕES, PONMANA SELVAN

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 $$ \phi(x) = \lambda \int_{0}^{1}(1+x+t) \, \phi(t) \, dt $$ and the nonhomogeneous equation $$ \phi(x) = x + \lambda \int_{0}^{1}(1+x+t) \, \phi(t) \, dt $$ for all $x \in [0,1]$ and $0<\lambda<\frac{2}{5}$.

Keywords: Hyers-Ulam stability, Hyers-Ulam-Rassias stability, Fredholm integral equation of second kind, fixed point theorem

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