The solution of a nonlinear integral equation with deviating argument based the on fixed point technique (Q2813840)

This paper is dedicated to the following nonlinear integral equation with deviating argument NEWLINE\[NEWLINE x(t)=f(t,x(\alpha(t)))+\int\limits_0^1 u(t,s,x(\alpha(s)))ds \tag{1} NEWLINE\]NEWLINE with respect to the unknown function \(x(t)\).NEWLINENEWLINEIn this work the existence of a solution of (1) is discussed. For this purpose the authors employ the fixed point theorem and Darbo condition with respect to a measure of noncompactness in the Banach space \(C[0,1]\).NEWLINENEWLINEThe numerical approach for Equation (1) based on sinc quadrature approximation is then suggested. Finally, these results are illustrated by five numerical examples.