Zalcman coefficient functional for tilted starlike functions with respect to conjugate points

Volume 29, Issue 1, pp 40--51 http://dx.doi.org/10.22436/jmcs.029.01.04

Publication Date: August 11, 2022 Submission Date: May 23, 2022 Revision Date: June 18, 2022 Accteptance Date: June 16, 2022

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Authors

D. Mohamed - Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia. N. H. A. A. Wahid - Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia.

Abstract

In this paper, we consider a subclass of tilted starlike functions with respect to conjugate points in an open unit disk. For functions in this subclass, we obtain the upper bounds for the initial coefficients and the Zalcman coefficient functional. Furthermore, we present several (known or new) consequences of our results based on the special choices of the involved parameters.

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Keywords

• Univalent functions
• starlike functions with respect to conjugate points
• coefficient estimates
• Zalcman conjecture
• subordination

MSC

•  30C45
•  30C50

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