Khan Bilal, Gong Jianhua, Khan Muhammad Ghaffar, Tchier Fairouz
Institute of Mathematics, Henan Academy of Sciences, Zhengzhou 450046, China.
Department of Mathematical Sciences, United Arab Emirates University, Al Ain 15551, United Arab Emirates.
Heliyon. 2024 Oct 4;10(19):e38838. doi: 10.1016/j.heliyon.2024.e38838. eCollection 2024 Oct 15.
Recent research has extensively explored classes of starlike and convex functions across various domains. This study introduces a novel class of symmetric starlike functions with respect to symmetric points and associated with the balloon shape domain. We establish the explicit representation of all functions in this class. We determine the sharp bounds for the initial four coefficients, the sharp Fekete-Szegö inequality, and the sharp bound for the second Hankel determinant for every function in the newly defined class. Furthermore, we present the new findings on the inverse and logarithmic coefficients sharp bounds for all functions belonging to this class.
近期的研究广泛探索了各类星形函数和凸函数在不同领域的情况。本研究引入了一类关于对称点且与气球形状域相关的新型对称星形函数。我们建立了该类中所有函数的显式表示。我们确定了该类中每个函数的前四个系数的精确界、精确的费克特 - 塞格不等式以及第二个汉克尔行列式的精确界。此外，我们给出了该类中所有函数的逆系数和对数系数精确界的新发现。
