EXACT ESTIMATES OF REGULAR FUNCTIONS AND RADII OF CONVEXITY AND STARLIKENESS OF SOME CLASSES OF STARLIKE AND CLOSE-TO-STARLIKE FUNCTIONS
ЖҰЛДЫЗ ПІШІНДІ, ЖАРТЫЛАЙ ЖҰЛДЫЗ ПІШІНДІ ФУНКЦИЯЛАРДЫҢ КЕЙБІР СЫНЫПТАРЫНЫҢ ДӨҢЕС РАДИУСЫ МЕН ЖҰЛДЫЗ ПІШІНДІЛІГІН ЖӘНЕ ТҰРАҚТЫ ФУНКЦИЯНЫ НАҚТЫ БАҒАЛАУ
ТОЧНЫЕ ОЦЕНКИ РЕГУЛЯРНЫХ ФУНКЦИЙ И РАДИУСЫ ВЫПУКЛОСТИ И ЗВЕЗДООБРАЗНОСТИ НЕКОТОРЫХ КЛАССОВ ЗВЕЗДООБРАЗНЫХ И ПОЧТИ ЗВЕЗДООБРАЗНЫХ ФУНКЦИЙ
Maiyer F.F. Tastanov M.G. Utemissova A.A. Ysmagul R.S.
2024Kazakh-British Technical University
Herald of the Kazakh British Technical UNiversity
2024#21Issue 2127 - 138 pp.
It is known that many problems for subclasses of univalent functions can be transformed into problems of minimizing or maximizing some functionals associated with the studied subclasses of univalent functions. Often, the logarithmic derivative of regular functions acts as such a functional. In this paper, we introduce a two-parameter subclass of functions regular in the unit circle with a positive real part, the expansion into a series of which begins with the nth degree. This class generalizes the well-known R.Goel and D.Shaffer class of regular functions whose values are contained in a circle symmetric with respect to the real axis containing the point 0 on the boundary. In this class of functions, exact estimates of various functionals, including the logarithmic derivative, are obtained. As applications of these estimates, the exact radii of convexity (or starlikeness) of various classes of starlike and close-to-starlike functions given using the class are found. All the results obtained are accurate and generalize many of the previously known results. The application of the estimates obtained in the article is promising, as it contributes to the theory of extreme problems associated with various subclasses of univalent functions.
estimates of regular functions , radius of convexity , radius of starlikeness , starlike functions , univalent functions
Text of the article Перейти на текст статьи
Non-commercial joint-stock company «Akhmet Baitursynuly Kostanay Regional University», Kostanay, 110000, Kazakhstan
Non-commercial joint-stock company «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