# Convolution operators in the geometric function theory

Zahid Shareef, Saqib Hussain, Maslina Darus

Research output: Contribution to journalArticle

7 Citations (Scopus)

### Abstract

The study of operators plays a vital role in mathematics. To define an operator using the convolution theory, and then study its properties, is one of the hot areas of current ongoing research in the geometric function theory and its related fields. In this survey-type article, we discuss historic development and exploit the strengths and properties of some differential and integral convolution operators introduced and studied in the geometric function theory. It is hoped that this article will be beneficial for the graduate students and researchers who intend to start work in this field. MSC: 30C45, 30C50.

Original language English 213 Journal of Inequalities and Applications 2012 https://doi.org/10.1186/1029-242X-2012-213 Published - 2012

### Fingerprint

Convolution Operator
Convolution
Mathematical operators
Operator
Integral Operator
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### Keywords

• analytic functions
• convolution
• differential operator
• hypergeometric function
• integral operator

### ASJC Scopus subject areas

• Analysis
• Applied Mathematics
• Discrete Mathematics and Combinatorics

### Cite this

Convolution operators in the geometric function theory. / Shareef, Zahid; Hussain, Saqib; Darus, Maslina.

In: Journal of Inequalities and Applications, Vol. 2012, 213, 2012.

Research output: Contribution to journalArticle

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AB - The study of operators plays a vital role in mathematics. To define an operator using the convolution theory, and then study its properties, is one of the hot areas of current ongoing research in the geometric function theory and its related fields. In this survey-type article, we discuss historic development and exploit the strengths and properties of some differential and integral convolution operators introduced and studied in the geometric function theory. It is hoped that this article will be beneficial for the graduate students and researchers who intend to start work in this field. MSC: 30C45, 30C50.

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