Convolution Properties of p-Valent Functions Associated with a Generalization of the Srivastava-Attiya Operator. (7th February 2013) - Gochhayat, Priyabrat
Abstract : Let 𝒜 p denote the class of functions analytic in the open unit disc 𝕌 and given by the series f ( z ) = z p + ∑ n = p + 1 ∞ a n z n . For f ∈ 𝒜 p, the transformation ℐ p, δ λ : 𝒜 p → 𝒜 p defined by ℐ p, δ λ f ( z ) = z p + ∑ n = p + 1 ∞ ( ( p + δ ) / ( n + δ ) ) λ a n z n,    ( δ + p ∈ ℂ ∖ ℤ 0 -,    λ ∈ ℂ ;    z ∈ 𝕌 ), has been recently studied as fractional differintegral operator by Mishra and Gochhayat (2010). In the present paper, we observed that ℐ p, δ λ 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.