Coefficient functionals for a class of bounded turning functions connected to three leaf function

Volume 28, Issue 3, pp 213--223 http://dx.doi.org/10.22436/jmcs.028.03.01

Publication Date: June 26, 2022 Submission Date: December 03, 2021 Revision Date: December 18, 2021 Accteptance Date: December 29, 2021

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Authors

G. Murugusundaramoorthy - School of Advanced Sciences, Vellore Institute of Technology, Vellore , India. M. G. Khan - Institute of Numerical Sciencies, Kohat University of Science and Technology, Kohat, Pakistan. B. Ahmad - Government Degree College Mardan HED KP, Mardan, 23200, Pakistan. V. K. Mashwani - Institute of Numerical Sciencies , Kohat University of Science and Technology, Kohat, Pakistan. T. Abdeljawad - Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, 111586, Saudi Arabia. - Department of Medical Research , China Medical University, Taichung, 40402, Taiwan. Z. Salleh - Department of Mathematics, Feculty of Ocean Engineering Technology and Informatics, University Malaysia Terengganu, Kaula Nerus, 21030, Terengganu, Malaysia.

Abstract

In this article, we define the class of bounded turning functions connected with three leaf function to investigate results for the estimates of four initial coefficients, Fekete-Szegö functional, the second-order Hankel determinant and Zalcman conjecture and these results are shown to be sharp. Furthermore, we estimate the bounds of the third-order Hankel determinants for this class and for its 2-fold and 3-fold symmetric functions. Finally we evaluate the sharp Krushkal inequality for the functions in this class.

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Keywords

• Analytic functions
• three leaf function
• subordination
• Hankel determinant
• invex set
• Zalcman conjuncture
• Krushkal inequality

MSC

•  30C45
•  30D30

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