A Fixed Point Approach to the Stability of an Integral Equation Related to the Wave Equation

Abstract

We will apply the fixed point method for proving the generalized Hyers-Ulam stability of the integral equation $\left(1/2c\right){\int }_{x-ct}^{x+ct}u\left(\tau ,t_0\right)d\tau =u\left(x,t\right)$ which is strongly related to the wave equation.