Some properties of certain subclass of meromorphically multivalent functions defined by linear operator

F. Ghanim, Maslina Darus

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

Problem statement: By means of the Hadamard product (or convolution), a linear operator was introduced. This operator was motivated by many authors namely Srivastava, Swaminathan, Owa and many others. The operator was indeed needed to create new ideas in the area of geometric function theory. Approach: The linear operator of meromorphic p-valent functions was proposed and defined. The preliminary concept of subordination was introduced to give sharp proofs for certain sufficient conditions of the linear operator aforementioned. Results: Having the operator, subordination theorems established by using standard concept of subordination and reduced to well-known results studied by various authors. The operator was then applied for fractional calculus and obtained new subordination theorem. Conclusion: Therefore, interesting operators could be obtained with some earlier results and standard methods.

Original languageEnglish
Pages (from-to)34-41
Number of pages8
JournalJournal of Mathematics and Statistics
Volume6
Issue number1
Publication statusPublished - 2010

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Multivalent Functions
Subordination
Linear Operator
Operator
Hadamard Product (or convolution)
P-valent Functions
Fractional Calculus
Meromorphic Function
Theorem
Sufficient Conditions

Keywords

  • Hadamard product
  • Hypergeometric
  • Linear operator
  • Meromorphic

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

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AB - Problem statement: By means of the Hadamard product (or convolution), a linear operator was introduced. This operator was motivated by many authors namely Srivastava, Swaminathan, Owa and many others. The operator was indeed needed to create new ideas in the area of geometric function theory. Approach: The linear operator of meromorphic p-valent functions was proposed and defined. The preliminary concept of subordination was introduced to give sharp proofs for certain sufficient conditions of the linear operator aforementioned. Results: Having the operator, subordination theorems established by using standard concept of subordination and reduced to well-known results studied by various authors. The operator was then applied for fractional calculus and obtained new subordination theorem. Conclusion: Therefore, interesting operators could be obtained with some earlier results and standard methods.

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