Some properties of differential operator to the subclass of univalent functions with negative coefficients

Volume 29, Issue 3, pp 295--305 https://doi.org/10.22436/jmcs.029.03.08

Publication Date: November 02, 2022 Submission Date: April 10, 2022 Revision Date: April 28, 2022 Accteptance Date: May 20, 2022

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Authors

K. Sridevi - Department of Mathematics, Dr. B. R. Ambedkar Open University, Hyderabad- 500 033, Telangana, India. T. Swaroopa Rani - Department of Mathematics, Dr. B. R. Ambedkar Open University, Hyderabad- 500 033, Telangana, India.

Abstract

Various function theorists have successfully defined and investigated different kinds of analytic functions. The applications of such functions have played significant roles in geometry function theory as a field of complex analysis. In this work, therefore, a certain subclass of univalent analytic functions is defined using a generalized differential operator and we have discussed a subclass \(TS_{\sigma, \delta} ^{~ \wp} (\vartheta ,\hbar ,\ell )\) of univalent functions with negative coefficients related to differential operator in the unit disk \( \mathbb { U }=\left \{{z \in \mathbb{ C }:|z|<1}\right \}\). We obtain basic properties like coefficient inequality, distortion and covering theorem, radii of starlikeness, convexity and close-to-convexity, extreme points, Hadamard product, and closure theorems for functions belonging to our class.

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Keywords

• Univalent
• differential operator
• starlike
• extreme points
• Hadamard product

MSC

•  30C45
•  30C50

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