  This paper revisits the well-studied fixed point problem from a unified
viewpoint of mathematical modeling and canonical duality theory, i.e. the
original problem is first reformulated as a nonconvex optimization problem, its
well-posedness is discussed based on objectivity principle in continuum
physics; then the canonical duality theory is applied for solving this problem
to obtain not only all fixed points, but also their stability properties.
Applications are illustrated by challenging problems governed by nonconvex
polynomial, exponential, and logarithmic operators. This paper shows that
within the framework of the canonical duality theory, there is no difference
between the fixed point problems and nonconvex analysis/optimization in
multidisciplinary studies.
