  Let T be a self-map on a metric space (X, d). Then T is called the Kannan map
if there exists \alpha, 0 < \alpha < 1/2, such that d(T(x), T(y)) <=
\alpha[d(x, T(x)) + d(y, T(y))], for all x, y in X.
  This paper aims to introduce a new method to construct fractal functions
using Kannan mappings. First, we give the rigorous construction of fractal
functions with the help of the Kannan iterated function system (IFS). We also
show the existence of a Borel probability measure supported on the attractor of
the Kannan IFS satisfying the strong separation condition. Moreover, we study
the smoothness of the constructed fractal functions. We end the paper with some
examples and graphical illustrations.
