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

Abstract

Consider an ordered Banach space and f,gf,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.

Keywords

• coincidence points
• banach spaces
• monotone operators
• matrix equations
• 54h25
• 47h07
• 39b42