For every
and
we define a class of analytic
functions, so-called
q-starlike functions of order
, on the open unit
disk. We study this class of functions and explore the relationships with other
well-known classes of analytic functions. The paper is also devoted to the
discussion on the Herglotz representation formula for analytic functions
when
... [Show full abstract] f(z) is q-starlike of order . We also consider
the concept of q-integrals and as a result we find a function that maximizes
the coefficients of power series of q-starlike functions of order .
As an application to special functions we obtain the order of q-starlikeness
of the shifted basic hypergeometric functions for certain
real values of a,b,c.