Аннотация: Геометрическая теория аналитических функций (ГТАФ) является привлекательной частью комплексного анализа, взаимосвязанная с другими разделами математики. Его основная цель состоит в том, чтобы определить различные классы геометрических аналитических функций и обсудить их геометрические свойства. В дальнейшем появилась взаимосвязь между теорией операторов и ГТАФ, которая до сих пор привлекает широкое внимание. В прошлом столетии теория операторов была распространена на открытый единичный круг комплексной плоскости и применялась для предложения разнообразных обобщений нормализованных аналитических функций. В результате теория операторов оказалась хорошим способом исследования в области ГТАФ. С тех пор изучение геометрических свойств с помощью операторов стало важной темой исследований. Настоящее исследование сосредоточено на изучении свойства выпуклости в классах \(\ell\)-равномерно выпуклых и звездообразных функций порядка \(\beta\) с использованием модифицированного интегро-дифференциального оператора Бриза в единичном круге. Кроме того, в классе аналитических функций рассматриваются некоторые условия, обеспечивающие звездообразность оператора Бриза.
Образец цитирования: Al-Janaby, H. F. and Ghanim, F. An Analysis of Convexity and Starlikeness Attributes for Breaz Integro-Differential Operator // Владикавк. мат. журн. 2022. Т. 24, № 2. C.25-34 (in English). DOI 10.46698/p4155-0765-8236-d
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