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) given by F(a,b;c;z)[email protected]?n=0~(a,n)(b,n)(c,n)(1,n)z^n,|z|<1, the author aims at finding conditions on a,b and c 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.

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