Approximate computation of the positive eigenvalue of a positive operator with a nonlinear occurrence of a parameter

A method is indicated for the approximate determination of the positive eigenvalue of the problem $x-Q_\lambda x=0$, $\lambda>0$, $x\in K$, $x\ne0$, where $K$ is a cone in Banach space and $Q_\lambda$ is an operator-valued function positive relative to $K$.