Abubakar Ahmad A, Matarneh Khaled, Al-Shaikh Suha B, Khan Mohammad Faisal, 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 Oct 9;10(20):e38960. doi: 10.1016/j.heliyon.2024.e38960. eCollection 2024 Oct 30.
In this article, by applying the convolution principle and symmetric -calculus, we develop a new generalized symmetric -difference operator of convolution type, which is applicable in the domain . Utilizing this operator, we construct, analyze, and evaluate two new sets of meromorphically harmonic functions in the Janowski domain. Furthermore, we investigate the convolution properties and necessary conditions for a function to belong to the class , examining the sufficiency conditions for to satisfy these properties. Moreover, we examine key geometric properties of the function in the class , including the distortion bound, convex combinations, the extreme point theorem, and weighted mean estimates.
在本文中，通过应用卷积原理和对称微积分，我们开发了一种新的卷积型广义对称差分算子，它适用于域 。利用这个算子，我们在Janowski域中构造、分析并评估了两组新的亚纯调和函数。此外，我们研究了函数 属于该类的卷积性质和必要条件，考察了 满足这些性质的充分条件。而且，我们研究了该类中函数 的关键几何性质，包括偏差界、凸组合、极值点定理和加权均值估计。
