BIRLIK DOIRADA ANALITIK FUNKSIYALAR UCHUN YUQORI TARTIBLI DIFFERENSIAL SUBKOORDINATSIYA VA SUPERORDINATSIYA XOSSALARI
DOI:
https://doi.org/10.5281/zenodo.21512487Ключевые слова:
differensial subkoordinatsiya; differensial superordinatsiya; Sălăgean operatori; yulduzsimon funksiya; konveks funksiya; bir yaproqli funksiya; dominantlar metodi; analitik funksiya; birlik doiraАннотация
Ushbu maqolada birlik doira (U = {z ∈ ℂ : |z| < 1}) da aniqlangan normallangan analitik
funksiyalarning (A) sinfi uchun yuqori tartibli differensial subkoordinatsiya va superordinatsiya nazariyasi tadqiq
etiladi. Tadqiqotning asosiy maqsadi Miller-Mocanu differensial subkoordinatsiya apparatini Sălăgean differensial
operatori yordamida umumlashtirish hamda yangi funksiyalar sinflarining geometrik xossalarini, jumladan,
yulduzsimonlik, konvekslik va bir yaproqlilik radiuslarini aniqlashdan iborat. Maqolada (Sn^*(\alpha)) va (Kn(\
alpha)) sinflarining parametrik tavsifi keltirilgan bo‘lib, bunda (n) operatorning tartibini, (\alpha\in[0,1)) esa tartib
parametrini ifodalaydi. Tadqiqotda Koebe funksiyasi asosida aniqlangan dominantlar metodidan foydalanilgan.
Mazkur yondashuv Miller-Mocanuning klassik natijalarini to‘ldiradi va umumlashtiradi. Asosiy teoremada
(p(z)\prec h(z)) subkoordinatsiya sharti bajarilishi hamda (\Psi) operatorining tegishli joiz funksiyalar sinfiga
mansubligi asosida yulduzsimonlikning yetarli shartlari aniqlangan. Olingan natijalar O‘zbekiston matematika
maktabining 2022-2024-yillardagi ilmiy ishlanmalari, xususan, Sa’dullayev va Abdullayevning tadqiqotlari bilan
muvofiqlashtirilgan hamda yangi funksiyalar sinflarining to‘liq tavsifi berilgan. Tadqiqot natijalaridan konformal
akslantirishlar nazariyasi va integral operatorlarning geometrik nazariyasida foydalanish mumkin
Библиографические ссылки
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