Research Article The Sharp Upper Bounds of the Hankel Determinant on Logarithmic Coefficients for Certain Analytic Functions Connected with Eight-Shaped Domains Pongsakorn Sunthrayuth , 1 Naveed Iqbal , 2 Muhammad Naeem , 3 Yousef Jawarneh, 2 and Sallieu K. Samura 4 1 Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT) Thanyaburi, Pathum Thani, Thailand 2 Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia 3 Deanship of Joint First Year Umm Al-Qura University Makkah, P.O. Box 715, Saudi Arabia 4 Department of Mathematics and Statistics, Fourah Bay College, University of Sierra Leone, Sierra Leone Correspondence should be addressed to Muhammad Naeem; mfaridoon@uqu.edu.sa and Sallieu K. Samura; sallieu.samura@usl.edu.sl Received 20 June 2022; Accepted 24 August 2022; Published 9 September 2022 Academic Editor: Mohsan Raza Copyright © 2022 Pongsakorn Sunthrayuth et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The present study’s intention is to produce exact estimations of some problems involving logarithmic coefficients for functions belonging to the considered subcollection BT sin of the bounded turning class. Furthermore, for the class BT sin , we look into the accurate bounds of the Zalcman inequality, Fekete-Szegö inequality along with D 2,1 ðG g /2Þ and D 2,2 ðG g /2Þ. Importantly, all of these bounds are shown to be sharp. 1. Introduction and Definitions To properly understand the findings provided in the article, certain important literature on Geometric Function Theory must first be discussed. In this regard, the letters S and A stand for the normalized univalent functions class and the normalized holomorphic (or analytic) functions class, respectively. These primary notions are defined in the region E d = fz ∈ ℂ : jzj <1g by A = g ∈ H E d ð Þ: gz ðÞ = z + 〠 ∞ k=2 b k z k z ∈ E d ð Þ ( ) , ð1Þ where H ðE d Þ symbolizes the holomorphic functions class, and S = g ∈ A : g is univalent in E d f g: ð2Þ The following formula defines the logarithmic coeffi- cients β n of g that belong to S G g z ðÞ ≔ log gz ðÞ z  =2 〠 ∞ n=1 β n z n for z ∈ E d : ð3Þ In many estimations, these coefficients provide a signifi- cant contribution to the concept of univalent functions. In 1985, De Branges [1] proved that 〠 n k=1 kn − k +1 ð Þ β n j j 2 ≤ 〠 n k=1 n − k +1 k ∀n ≥ 1, ð4Þ and equality will be achieved if g has the form z/ð1 − e iθ zÞ 2 for some θ ∈ ℝ: In its most comprehensive version, this inequality offers the famous Bieberbach-Robertson-Milin conjectures regarding Taylor coefficients of g ∈ S . We refer Hindawi Journal of Function Spaces Volume 2022, Article ID 2229960, 12 pages https://doi.org/10.1155/2022/2229960