On new bijective convolution operator acting for analytic functions

Oqlah Al-Refai, Maslina Darus

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Problem statement: We introduced a new bijective convolution linear operator defined on the class of normalized analytic functions. This operator was motivated by many researchers namely Srivastava, Owa, Ruscheweyh and many others. The operator was essential to obtain new classes of analytic functions. Approach: Simple technique of Ruscheweyh was used in our preliminary approach to create new bijective convolution linear operator. The preliminary concept of Hadamard products was mentioned and the concept of subordination was given to give sharp proofs for certain sufficient conditions of the linear operator aforementioned. In fact, the subordinating factor sequence was used to derive different types of subordination results. Results: Having the linear operator, subordination theorems were established by using standard concept of subordination. The results reduced to well-known results studied by various researchers. Coefficient bounds and inclusion properties, growth and closure theorems for some subclasses were also obtained. Conclusion: Therefore, many interesting results could be obtained and some applications could be gathered.

Original languageEnglish
Pages (from-to)77-87
Number of pages11
JournalJournal of Mathematics and Statistics
Volume5
Issue number1
DOIs
Publication statusPublished - 2009

Fingerprint

Convolution Operator
Bijective
Subordination
Analytic function
Linear Operator
Coefficient Bounds
Hadamard Product
Operator
Theorem
Closure
Inclusion
Sufficient Conditions
Concepts

Keywords

  • Convex functions
  • Convolution
  • Prestarlike functions
  • Starlike functions
  • Subordinations

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

On new bijective convolution operator acting for analytic functions. / Al-Refai, Oqlah; Darus, Maslina.

In: Journal of Mathematics and Statistics, Vol. 5, No. 1, 2009, p. 77-87.

Research output: Contribution to journalArticle

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