Abstract
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.
Highlights
Let A denote the class of functions of the form ∞f (z) = z + anzn, ( . ) n=which are analytic in the open unit disc E = {z : |z| < }, centered at origin and normalized by the conditions f ( ) = and f ( ) =
Many differential and integral operators can be written in terms of convolution of certain analytic functions
3 Concluding remarks The operation of convolution and convolution operators are the topics of great interest for researchers
Summary
Many differential and integral operators can be written in terms of convolution of certain analytic functions. This shows how differential and integral operators may be written in terms of convolution of functions. 2.2 Ruscheweyh derivative operator (1975) Using the technique of convolution, Ruscheweyh [ ] defined the operator Dλ on the class of analytic functions A as See, for example, [ – ], have used the Ruscheweyh operator to define and investigate the properties of certain known and new classes of analytic functions.
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