# Sufficient conditions for subordination of meromorphic functions

Rabha W. Ibrahim, Maslina Darus

Research output: Contribution to journalArticle

3 Citations (Scopus)

### Abstract

Problem statement: The problem of giving sufficient condition for certain class of meromorphic functions defined as differential operator was studied. Approach: The differential operator of meromorphic functions containing fractional power was proposed and defined. The preliminary concept of subordination was introduced to give sharp proofs for certain sufficient conditions of the differential operator aforementioned. Results: Having new operator, subordination theorems established by using standard concept of subordination and reduced to well-known results studied by various researchers. The operator was then applied for fractional calculus and obtained new subordination theorem. Conclusion: Therefore, by having new operators, new criteria and new set of subordination theorems could be obtained with some earlier results and standard methods.

Original language English 141-145 5 Journal of Mathematics and Statistics 5 3 https://doi.org/10.3844/jmssp.2009.141.145 Published - 2009

### Fingerprint

Subordination
Meromorphic Function
Sufficient Conditions
Differential operator
Operator
Theorem
Fractional Powers
Fractional Calculus

### Keywords

• Fractional calculus
• Meromorphic function
• Subordination

### ASJC Scopus subject areas

• Mathematics(all)
• Statistics and Probability

### Cite this

In: Journal of Mathematics and Statistics, Vol. 5, No. 3, 2009, p. 141-145.

Research output: Contribution to journalArticle

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AB - Problem statement: The problem of giving sufficient condition for certain class of meromorphic functions defined as differential operator was studied. Approach: The differential operator of meromorphic functions containing fractional power was proposed and defined. The preliminary concept of subordination was introduced to give sharp proofs for certain sufficient conditions of the differential operator aforementioned. Results: Having new operator, subordination theorems established by using standard concept of subordination and reduced to well-known results studied by various researchers. The operator was then applied for fractional calculus and obtained new subordination theorem. Conclusion: Therefore, by having new operators, new criteria and new set of subordination theorems could be obtained with some earlier results and standard methods.

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