Matarneh Khaled, Abubakar Ahmad A, Khan Mohammad Faisal, Al-Shaikh Suha B, Kamal Mustafa
Faculty of Computer Studies, Arab Open University, Riyadh, 11681, Saudi Arabia.
Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh, 11673, Saudi Arabia.
Heliyon. 2024 Jun 10;10(12):e32359. doi: 10.1016/j.heliyon.2024.e32359. eCollection 2024 Jun 30.
In this article, we make use of the concepts of subordination and the -calculus theory to analyze a new class of analytic bi-univalent functions associated to the cardioid domain. Our main focus is to derive a sharp inequality for a newly defined class of analytic and bi-univalent functions in the open unit disc . We explore the bounds of initial coefficients, Fekete-Szegö type problems, and coefficient inequalities for newly established families. In addition, we explore some recent findings for the bi-univalent function and inverse function. Additionally, a few well-known results are mentioned to help make links between earlier and current results.
在本文中，我们利用从属概念和(\lambda)-演算理论来分析与心形区域相关的一类新的解析双单叶函数。我们的主要重点是为开单位圆盘(\mathbb{D})中一类新定义的解析双单叶函数推导一个精确不等式。我们研究了初始系数的界、费克特 - 塞格类型问题以及新建立族的系数不等式。此外，我们探讨了双单叶函数及其逆函数的一些最新研究结果。另外，还提及了一些著名结果，以帮助建立早期结果与当前结果之间的联系。
