An application of a certain integral operator (Q1186959)

Let \(A_ p\) denote the class of functions of the form \(f(z)=z^ p+\sum^ \infty_{n=p+1}a_ nz^ n (p\in N=\{1,2,\ldots\})\) which are analytic in the open unit disk \(U=\{z:| z|<1\}\). For \(f\in A_ p\), the authors define the integral operator \(J_{c,p}\) by \(J_{c,p}(f(z))={c+p\over z^ c}\int^ z_ 0f(t)t^{c-1}dt\), \((c>- p)\) and study certain properties of the operator.