Sufficiency for hypergeometric transforms to be associated with conic regions

For a certain integral operator acting on the normalized Gaussian hypergeometric function zF(a,b;c;z)zF(a,b;c;z) given by F(a,b;c;z)=∑n=0∞(a,n)(b,n)(c,n)(1,n)zn,|z|<1, the author aims at finding conditions on a,ba,b and cc such that the operator maps certain subclasses of analytic functions into some other classes of functions that have nice geometric properties related to certain conic regions.