  This is a continuation of our previous work entitled \enquote{Alternating
Proximity Mapping Method for Convex-Concave Saddle-Point Problems}, in which we
proposed the alternating proximal mapping method and showed convergence results
on the sequence of our iterates, the sequence of averages of our iterates, and
the sequence of function values evaluated at the averages of the iterates for
solving convex-concave saddle-point problems.
  In this work, we extend the application of the alternating proximal mapping
method to solve strongly convex-strongly concave saddle-point problems. We
demonstrate two sets of sufficient conditions and also their simplified
versions, which guarantee the linear convergence of the sequence of iterates
towards a desired saddle-point. Additionally, we provide two sets of sufficient
conditions, along with their simplified versions, that ensure the linear
convergence of the sequence of function values evaluated at the convex
combinations of iteration points to the desired function value of a
saddle-point.
