kaz29Вестник Казахстанско-Британского технического университетаHerald of the Kazakh-British Technical University1998-66882959-8109Казахстанско-Британский Технический Университет10.55452/1998-6688-2024-21-4-168-185kaz29-1549Research ArticleМАТЕМАТИЧЕСКИЕ НАУКИMATHEMATICAL SCIENCESКЛАССЫ ПОЧТИ ЗВЕЗДООБРАЗНЫХ ФУНКЦИЙ, ПОСТРОЕННЫЕ НА ОСНОВЕ ОПОРНОЙ ФУНКЦИИ ОБЩЕГО ВИДАCLASSES OF CLOSE-TO-STARLIKE FUNCTIONS BASED ON THE REFERENCE FUNCTION OF A GENERAL FORMhttps://orcid.org/0000-0002-2278-2723МайерФ. Ф.MaiyerF. F.

канд. физ.-мат. наук, профессор

г. Костанай

Candidate of Physical and Mathematical Sciences, Professor

Kostanay

maiyer@mail.ruhttps://orcid.org/0000-0003-1926-8958ТастановМ. Г.TastanovM. G.

канд. физ.-мат. наук, профессор

г. Костанай

Candidate of Physical and Mathematical Sciences, Professor

Kostanay

tastao@mail.ruhttps://orcid.org/0000-0001-5143-0260УтемисоваА. А.UtemissovaA. A.

канд. пед. наук

г. Костанай

Candidate of Pedagogical Sciences

Kostanay

anar_utemisova@mail.ruhttps://orcid.org/0000-0002-6435-9560БайманкуловА. Т.BaimankulovA. Т.

докт. физ.-мат. наук, доцент

г. Костанай

Doctor of Physical and Mathematical Sciences, Associate Professor

Kostanay

g_talgat_a@mail.ruКостанайский региональный университет имени Ахмета БайтұрсынұлыКазахстанBaitursynuly Kostanay Regional UniversityKazakhstan202424122024214168185Copyright © Майер Ф.Ф., Тастанов М.Г., Утемисова А.А., Байманкулов А.Т., 20242024Майер Ф.Ф., Тастанов М.Г., Утемисова А.А., Байманкулов А.Т.Maiyer F.F., Tastanov M.G., Utemissova A.A., Baimankulov A.Т.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestnik.kbtu.edu.kz/jour/article/view/1549

Цель статьи – представить и исследовать широкий класс дважды почти звездообразных функций, продемонстрировав при этом единый подход к решению определенного круга экстремальных задач. В статье определена опорная функция общего вида – звездообразная функция, на базе которой можно строить классы почти звездообразных и дважды почти звездообразных функций. На базе опорной функции общего вида, содержащей три параметра, и новых оценок аналитических функций вводится обобщение различных подклассов классов почти звездообразных и дважды почти звездообразных функций, рассмотренных в ряде статей, вышедших в последние годы, в том числе введенный класс содержит обобщенный класс типично вещественных функций. Изучены свойства введенного класса функций, например, получены теорема роста, оценки модуля логарифмической производной функции и радиус звездообразности, в частных случаях приводящие как к ранее известным результатам, так и представляющие собой новые результаты. Все результаты статьи являются точными.

The purpose of the article is to introduce and explore a wide class of doubly close-to-starlike functions, while demonstrating a unified approach to solving a certain range of extreme problems. The article defines a reference function of a general form – a starlike function, on the basis of which classes of close-to-starlike and doubly close-to-starlike functions can be constructed. On the basis of a general support function containing three parameters and new estimates of analytical functions, a generalization of various classes of close-to-starlike and doubly close-to-starlike functions is introduced, considered in a number of articles published in recent years, including the introduced class contains a generalized class of typically real functions. The properties of the introduced class of functions are studied, for example, the growth theorem, estimates of the modulus of the logarithmic derivative of the function and the radius of starlikeness are obtained, in particular cases leading to previously known results and representing new results. All the results of the article are accurate.

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The authors declare that there are no conflicts of interest present.