Some properties of Noor integral operator (Q2775689)

Let \(A(p)\) denote the class of functions of the form NEWLINE\[NEWLINEf(z)= z^p+ \sum^\infty_{k=1} a_k z^{p+k}\quad (p\in\mathbb{N},\;\mathbb{N}= \{1,2,3,\dots\})NEWLINE\]NEWLINE which are analytic in the unit disc. If \(n>-p\) let \(f_{n+p-1}= z^p/(1- z)^{n+p}\), and \(f^{(-1)}_{n+ p-1}(z)\) be defined such that \(f_{n+p-1}(z)* f^{(-1)}_{n+ p-1}(z)= z^p/(1- z)^{p+1}\), where \(*\) denotes the Hadamard product. A new operator called by the authors ``Noor integral'' is defined based on the above definition and its properties are investigated.