Convolution Properties of p-Valent Functions Associated with a Generalization of the Srivastava-Attiya Operator. (7th February 2013)

• Record Type: Journal Article
• Authors: Gochhayat, Priyabrat
• Other Names: Dziok Jacek Academic Editor.
• Is Part Of: Journal of complex analysis. Volume 2013(2013)
• Publication Date: 2013-02-07
• Subjects: Functions of complex variables -- Periodicals; Mathematical analysis -- Periodicals; 515.905
• DOI: 10.1155/2013/676027
• Languages: English
• ISSNs: 2314-4963

Abstract

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.