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Consider an ordered Banach space andf,gf,gtwo self-operators defined on the interior of its positive cone. In this article, we prove that the equationf(X)=g(X)f(X)=g(X)has a positive solution, whenever  f  is strictlyα\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.

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