Journal of Mathematics and Statistics

On Certain Classes of Multivalent Analytic Functions

Rabha W. Ibrahim and Maslina Darus

DOI : 10.3844/jmssp.2010.271.275

Journal of Mathematics and Statistics

Volume 6, Issue 3

Pages 271-275


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.


© 2010 Rabha W. Ibrahim and Maslina Darus. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.