On a new generalized class of p-valent functions and its mapping conditions by a Wright's generalized hypergeometric operator

A new generalized class of p-valent functions

Résumé

A generalized class $R_{\gamma }^{\tau }(m,p,A,B)$ involving $(m-1)^{th}$ and $m^{th}$ derivatives of $p$-valent functions is defined and its integral representation, coefficient condition and a sufficient condition for a function to be in this class are obtained. Further, we investigate certain mapping properties of a Wright's generalized hypergeometric operator $Wf(z)$ related to the class $R_{\gamma }^{\tau }(m,p,A,B)$ with some other known classes.