Positive coincidence points for a class of nonlinear operators and their applications to matrix equations

Consider an ordered Banach space and f, g f,g two self-operators defined on the interior of its positive cone. In this article, we prove that the equation f (X) = g (X) f(X)=g(X) has a positive solution, whenever f is strictly α \alpha-concave g-monotone or strictly (-α) (-\alpha)-convex g-antitone with g super-homogeneous and surjective. As applications, we show the existence of positive definite solutions to new classes of nonlinear matrix equations.