Convolution Properties of p-Valent Functions Associated with a Generalization of the Srivastava-Attiya Operator

Abstract EN

Let ?p denote the class of functions analytic in the open unit disc ? and given by the series f(z)=zp+∑n=p+1∞anzn.

For f∈?p, the transformation ℐp,δλ:?p→?p defined by ℐp,δλf(z)=zp+∑n=p+1∞((p+δ)/(n+δ))λanzn, (δ+p∈ℂ∖ℤ0-, λ∈ℂ; z∈?), has been recently studied as fractional differintegral operator by Mishra and Gochhayat (2010).

In the present paper, we observed that ℐp,δλ can also be viewed as a generalization of the Srivastava-Attiya operator.

Convolution preserving properties for a class of multivalent analytic functions involving an adaptation of the popular Srivastava-Attiya transform are investigated.