Applications of Hilbert’s projective metric to a class of positive nonlinear operators

The purpose of this paper is to study the eigenvalue problems for a class of positive nonlinear operators. Using projective metric techniques and the contraction mapping principle, we establish existence, uniqueness and continuity results for positive eigensolutions of a particular type of positive nonlinear operator. In addition, we prove the existence of a unique fixed point of the operator with explicit norm-estimates. Applications to nonlinear systems of equations and to matrix equations are considered.