A Class of Multivalent Analytic Functions Defined by a New Linear Operator

Volume 8, Issue 4, pp 326-334 http://dx.doi.org/10.22436/jmcs.08.04.01

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Authors

Rahim Kargar - Department of Mathematics, Payame Noor University, I. R. of IRAN. Abdoljalil Bilavi - Department of Mathematics, Shoush Branch, Islamic Azad University, Shoush, Iran. Salahaddin Abdolahi - Department of Mathematics, Payame Noor University, I. R. of IRAN. Salah Maroufi - Department of Mathematics, Payame Noor University, I. R. of IRAN.

Abstract

The main object of the present paper is to derive some results for multivalent analytic functions defined by a linear operator. Making use of a certain operator, which is defined here by means of Hadamard product, we introduce a subclasses \(S_{A,B}^{p,\gamma}(\alpha,\lambda,\mu,\nu,a,c)\) of the class \(A(p)\) of normalized p-valent analytic functions on the open unit disk. Also we have extended some of the previous results and have given necessary and sufficient condition for this class.

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Keywords

• Analytic functions
• Multivalent functions
• Hadamard product
• Subordination
• Linear operators.

MSC

•  30C45
•  30C50

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