Khan Mohammad Faisal, Abaoud Mohammed, Ahmad Naeem, Almuqrin Muqrin A
Department of Basic Sciences, College of Science, and Theoretical Studies, Saudi Electronic University, Riyadh, Kingdom of Saudi Arabia.
Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia.
PLoS One. 2025 May 5;20(5):e0317339. doi: 10.1371/journal.pone.0317339. eCollection 2025.
Function theory research has long struggled with the challenge of deriving sharp estimates for the coefficients of analytic and univalent functions. Researchers have advanced the field by developing and applying a variety of approaches to get these bounds. In the current paper, we apply the technique of subordination, we define the family of symmetric starlike functions which is related to generating function of Gregory coefficients. We provide sharp bounds for the problem concerning the coefficients of the family of symmetric starlike functions connected to the generating function of Gregory coefficients by utilizing the notion of functions with positive real component. These problems include first five sharp coefficient bounds and Fekete-Szego problem along with the Hankel determinant of order three. Additionally, we explore the optimal bounds (sharp bounds) for two important functions, the logarithmic function and the inverse function within the same class of symmetric starlike functions which is related to generating function of Gregory coefficients.
函数理论研究长期以来一直面临着为解析单叶函数的系数推导精确估计值的挑战。研究人员通过开发和应用各种方法来获得这些界，推动了该领域的发展。在本文中，我们应用从属技术，定义了与格雷戈里系数生成函数相关的对称星形函数族。通过利用具有正实部的函数的概念，我们为与格雷戈里系数生成函数相关的对称星形函数族的系数问题提供了精确的界。这些问题包括前五个精确系数界、费克特 - 塞格问题以及三阶汉克尔行列式。此外，我们还探讨了与格雷戈里系数生成函数相关的同一类对称星形函数中两个重要函数，即对数函数和反函数的最优界（精确界）。
