  In [14,26], new approximation classes of self-referential functions are
introduced as fractal versions of the classes of polynomials and rational
functions. As a sequel, in the present article, we define a new approximation
class consisting of self-referential functions, referred to as the fractal
rational trigonometric functions. We establish Weierstrass type approximation
theorems for this class and prove the existence of a best fractal rational
trigonometric approximant to a real-valued continuous function on a compact
interval. Furthermore, we provide an upper bound for the smallest error in
approximating a prescribed continuous function by a fractal rational
trigonometric function. This extemporizes an analogous result in the context of
fractal rational function appeared in [26] and followed in the setting of
Bernstein fractal rational functions in [23]. The last part of the article aims
to clarify and correct the mathematical errors in some results on the Bernstein
alpha-fractal functions appeared recently in the literature [22-24].
