ABOUT SOME SUBCLASSES OF CLASSES OF CLOSE-TO-CONVEX AND DOUBLY CLOSE-TO-CONVEX FUNCTIONS
ДӨҢЕС ДЕРЛІК ЖӘНЕ ЕКІ ЕСЕ ДӨҢЕС ДЕРЛІК ФУНКЦИЯЛАР КЛАСЫНЫҢ КЕЙБІР ҚОСАЛҚЫ КЛАСТАРЫ ТУРАЛЫ
О НЕКОТОРЫХ ПОДКЛАССАХ КЛАССОВ ПОЧТИ ВЫПУКЛЫХ И ДВАЖДЫ ПОЧТИ ВЫПУКЛЫХ ФУНКЦИЙ
Maiyer F.F. Tastanov M.G. Utemissova A.A. Kalakov B.A.
2025Kazakh-British Technical University
Herald of the Kazakh British Technical UNiversity
2025#22Issue 4279 - 294 pp.
It is known that the class close-to-convex functions is defined by the condition of positivity of the functional (Formula Presented) with a starlike function g(z). Replacing the starlike function g(z) with a convex one leads to a known subclass of the class. In this article, we introduce a generalization of the class C’ to the case when the set of values (Formula Presented)is contained in a region of a special type, which, in a particular case, can coincide with a half-plane. The generalization is also associated with the extension of the class C’ to a certain subclass of the class of normalized doubly close-to-convex functions. The diversity of special cases of a domain of a special type and the transition to doubly close-to-convex functions allows us to obtain both new original results and generalizations of previously known results. The main research of this article is aimed at proving theorems on distortion, finding the radii of convexity of the considered classes of functions and justifying the accuracy of the obtained results. A connection has also been established between the introduced class of functions and a certain new class of doubly close-to-starlike functions, special cases of which have been actively studied in recent years. For this class and its subclasses, new results have also been obtained in the form of theorems on growth and radius of starlikeness and generalization of previously known results.
close-to-convex functions , close-to-starlike functions , distortion theorems , growth theorems , radii of convexity , radii of starlikeness , starlike functions
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Akhmet Baitursynuly Kostanay Regional University, Kostanay, Kazakhstan
Akhmet Baitursynuly Kostanay Regional University
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026