2013DOAJ (DOAJ: Directory of Open Access Journals)Open access

Families of Meromorphic Multivalent Functions Associated with the Dziok-Raina Operator

G. Murugusundaramoorthy, M. K. Aouf

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Abstract

Making use a linear operator, which is defined here by means of the Hadamard product (or convolution), involving the Wright’s generalized hypergeometric function , we introduce two novel subclassesP p(q,s,α1;A,B,λ) andP+p(q,s,α1;A,B,λ) of meromorphically multivalent functions oforder λ(0 ≤ λ < p) in the punctured disc U∗. In this paper we investigate the various important properties and characteristics of these subclasses of meromorphically multivalent functions. We extend the familiar concept of neighborhoods of analytic functions to these subclasses of meromorphically multivalent functions . We also derive many interesting results for the Hadamard products of functions belonging to the classP+p(q,s,α1;A,B,λ).

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Making use a linear operator, which is defined here by means of the Hadamard product (or convolution), involving the Wright’s generalized hypergeometric function , we introduce two novel subclassesP p(q,s,α1;A,B,λ) andP+p(q,s,α1;A,B,λ) of meromorphically multivalent functions oforder λ(0 ≤ λ < p) in the punctured disc U∗. In this paper we investigate the various important properties and characteristics of these subclasses of meromorphically multivalent functions. We extend the familiar concept of neighborhoods of analytic functions to these subclasses of meromorphically multivalent functions . We also derive many interesting results for the Hadamard products of functions belonging to the classP+p(q,s,α1;A,B,λ).

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Available abstract

Making use a linear operator, which is defined here by means of the Hadamard product (or convolution), involving the Wright’s generalized hypergeometric function , we introduce two novel subclassesP p(q,s,α1;A,B,λ) andP+p(q,s,α1;A,B,λ) of meromorphically multivalent functions oforder λ(0 ≤ λ < p) in the punctured disc U∗. In this paper we investigate the various important properties and characteristics of these subclasses of meromorphically multivalent functions. We extend the familiar concept of neighborhoods of analytic functions to these subclasses of meromorphically multivalent functions . We also derive many interesting results for the Hadamard products of functions belonging to the classP+p(q,s,α1;A,B,λ).

Key concepts: Meromorphic function, Operator (biology), Mathematics, Pure mathematics, Chemistry, Biochemistry, Transcription factor, Repressor

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