Research Article Open Access

On Certain Classes of Multivalent Analytic Functions

Rabha W. Ibrahim and Maslina Darus

Abstract

Problem statement: By means of the Hadamard product (or convolution), new class of function of power order was formed. This class was motivated by many authors namely MacGregor, Umezawa, Darus and Ibrahim and many others. The class indeed extended in the form of integral operator due to the work of Bernardi, Libera and Livingston. Approach: A new class of multivalent analytic functions in the open unit disk U was introduced. An application of this class was posed by using the fractional integral operator. The integral operator of multivalent functions was proposed and defined. The previous well known integral operator was mentioned. Results: Having the integral operator, a class was defined and coefficient bounds established by using standard method. These results reduced to well-known results studied by various authors. The operator was then applied for fractional calculus and obtained the coefficient bounds. Conclusion: Therefore, new operators could be obtained with some earlier results and standard methods. New classes were formed and new results of special cases were obtained.

Journal of Mathematics and Statistics
Volume 6 No. 3, 2010, 271-275

DOI: https://doi.org/10.3844/jmssp.2010.271.275

Submitted On: 30 May 2010 Published On: 30 September 2010

How to Cite: Ibrahim, R. W. & Darus, M. (2010). On Certain Classes of Multivalent Analytic Functions. Journal of Mathematics and Statistics, 6(3), 271-275. https://doi.org/10.3844/jmssp.2010.271.275

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Keywords

  • Multivalent analytic function
  • Hadamard product
  • fractional integral operator
  • multiplier transformation
  • starlike function
  • convex function