  In this paper we consider basic hypergeometric functions introduced by Heine.
We study mapping properties of certain ratios of basic hypergeometric functions
having shifted parameters and show that they map the domains of analyticity
onto domains convex in the direction of the imaginary axis. In order to
investigate these mapping properties, few useful identities are obtained in
terms of basic hypergeometric functions. In addition, we find conditions under
which the basic hypergeometric functions are in $q$-close-to-convex family.
