Hadi Sarem H, Shaba Timilehin Gideon, Madhi Zainab S, Darus Maslina, Lupaş Alina Alb, Tchier Fairouz
Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq.
Department of Business Management, Al-imam University College, Balad 34011, Iraq.
MethodsX. 2024 Jul 3;13:102842. doi: 10.1016/j.mex.2024.102842. eCollection 2024 Dec.
The study of holomorphic functions has been recently extended through the application of diverse techniques, among which quantum calculus stands out due to its wide-ranging applications across various scientific disciplines. In this context, we introduce a novel q-differential operator defined via the generalized binomial series, which leads to the derivation of new classes of quantum-convex (q-convex) functions. Several specific instances within these classes were explored in detail. Consequently, the boundary values of the Hankel determinants associated with these functions were analyzed. All graphical representations and computational analyses were performed using Mathematica 12.0.•These classes are defined by utilizing a new q-differential operator.•The coefficient values are investigated.•Toeplitz determinants, such as the second and the third order inequalities, are calculated.
全纯函数的研究最近通过多种技术的应用得到了扩展，其中量子微积分因其在各个科学学科中的广泛应用而脱颖而出。在此背景下，我们引入了一个通过广义二项式级数定义的新型q - 微分算子，这导致了新的量子凸（q - 凸）函数类别的推导。详细探讨了这些类别中的几个具体实例。因此，分析了与这些函数相关的汉克尔行列式的边界值。所有图形表示和计算分析均使用Mathematica 12.0进行。
• 这些类别是通过使用新的q - 微分算子定义的。
• 研究了系数值。
• 计算了托普利兹行列式，如二阶和三阶不等式。
