On certain classes of multivalent analytic functions

Rabha W. Ibrahim, Maslina Darus

Research output: Contribution to journalArticle

4 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)271-275
Number of pages5
JournalJournal of Mathematics and Statistics
Volume6
Issue number3
Publication statusPublished - 2010

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Multivalent Functions
Analytic function
Integral Operator
Coefficient Bounds
Hadamard Product (or convolution)
Fractional Integral Operator
Fractional Calculus
Operator
Class
Unit Disk

Keywords

  • Convex function
  • Fractional integral operator
  • Hadamard product
  • Multiplier transformation
  • Multivalent analytic function
  • Starlike function

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

On certain classes of multivalent analytic functions. / Ibrahim, Rabha W.; Darus, Maslina.

In: Journal of Mathematics and Statistics, Vol. 6, No. 3, 2010, p. 271-275.

Research output: Contribution to journalArticle

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