# Third Hankel determinant and Zalcman functional for a class of starlike functions with respect to symmetric points related with sine function

Volume 25, Issue 1, pp 29--36
Publication Date: May 04, 2021 Submission Date: January 21, 2021 Revision Date: April 03, 2021 Accteptance Date: April 07, 2021
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### Authors

Muhammad Ghaffar Khan - Institute of Numerical Sciences, Kohat University of Science and Technology, Kohat, Pakistan. Bakhtiar Ahmad - AhmadGovt. Degree College Mardan, 23200 Mardan, Pakistan. Gangadharan Murugusundaramoorthy - Department of Mathematics, School of Advanced Sciences, Vellore Institute Technology University Vellore - 632014, India. Wali Khan Mashwani - Institute of Numerical Sciences, Kohat University of Science and Technology, Kohat, Pakistan. Sibel Yalçin - Department of Mathematics, Faculty of Arts and Sciences, Bursa Uludag University, 16059, Bursa, Turkey. Timilehin Gideon Shaba - Department of Mathematics, Physical Sciences, University of Ilorin, Nigeria. Zabidin Salleh - Department of Mathematics, Faculty of Ocean Engineering Technology and Informatics, University Malaysia Terengganu, 21030 Kuala Nerus, Terenggunu, Malaysia.

### Abstract

In this article we define a class of starlike functions with respect to symmetric points in the domain of sine function. Also, we investigate coefficients bounds and upper bounds for the third order Hankel determinant for this defined class. We also evaluate the Zalcman functional $|a_{3}^{2}-a_{5}|$. Specializing the parameters, we improve Zalcman functional for the class of starlike functions.

### Share and Cite

##### ISRP Style

Muhammad Ghaffar Khan, Bakhtiar Ahmad, Gangadharan Murugusundaramoorthy, Wali Khan Mashwani, Sibel Yalçin, Timilehin Gideon Shaba, Zabidin Salleh, Third Hankel determinant and Zalcman functional for a class of starlike functions with respect to symmetric points related with sine function, Journal of Mathematics and Computer Science, 25 (2022), no. 1, 29--36

##### AMA Style

Khan Muhammad Ghaffar, Ahmad Bakhtiar, Murugusundaramoorthy Gangadharan, Mashwani Wali Khan, Yalçin Sibel, Shaba Timilehin Gideon, Salleh Zabidin, Third Hankel determinant and Zalcman functional for a class of starlike functions with respect to symmetric points related with sine function. J Math Comput SCI-JM. (2022); 25(1):29--36

##### Chicago/Turabian Style

Khan, Muhammad Ghaffar, Ahmad, Bakhtiar, Murugusundaramoorthy, Gangadharan, Mashwani, Wali Khan, Yalçin, Sibel, Shaba, Timilehin Gideon, Salleh, Zabidin. "Third Hankel determinant and Zalcman functional for a class of starlike functions with respect to symmetric points related with sine function." Journal of Mathematics and Computer Science, 25, no. 1 (2022): 29--36

### Keywords

• Analytic functions
• subordinations
• sine function
• Hankel determinant
• Zalcman functional

•  30C45
•  30C50