q–differ-integral operator on p–valent functions associated with operator on Hilbert space

Abstract

Making use of multivalent functions with negative coefficients of the type f(z) = z^p − ∑ ^∞_{k = p+1} a_kz^k, which are analytic in the open unit disk and applying the q-derivative a q–differ-integral operator is considered. Furthermore by using the familiar Riesz-Dunford integral, a linear operator on Hilbert space H is introduced. A new subclass of p-valent functions related to an operator on H is defined. Coefficient estimate, distortion bound and extreme points are obtained. The convolution-preserving property is also investigated.