On existence of extremal solutions of nonlinear functional integral equations in Banach algebras (Q1769362)

Let \(K\) be a normal and positive cone of a real Banach algebra \(X\) and let \(u\), \(v\in X\) be such that \(u\leq v\). The author proves the existence of a least solution and a greatest one of the operator equation \[ AxBx+Cx=x \] in \([u,v]\), where \(A\), \(B:[u,v]\to K\) and \(C:[u,v]\to X\) satisfy some suitable conditions. Applications to a functional integral equation of mixed type are also given.