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

Abstract

Let 𝒜p denote the class of functions analytic in the open unit disc 𝕌 and given by the series f(z)=zp+∑n=p+1∞anzn. For f∈𝒜p, the transformation ℐp,δλ:𝒜p→𝒜p defined by ℐp,δλf(z)=zp+∑n=p+1∞((p+δ)/(n+δ))λanzn, (δ+p∈ℂ∖ℤ0-, λ∈ℂ; z∈𝕌), 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.

Third-Order Differential Subordination and Differential Superordination Results for Analytic Functions Involving the Srivastava-Attiya Operator

“…Various applications of J µ,b f (z) are found in [3,5,7,6,12,21] and the references therein. From (1.6), it is clear that…”

“…The operator J µ,b f (z) is now popularly known in the literature as the Srivastava-Attiya operator. Various applications of J µ,b f (z) are found in [3,5,7,6,12,21] and the references therein. From (1.6), it is clear that…”