Sharp estimate of the fifth coefficients for the class U(lambda)

	Sharp estimate of the fifth coefficients for the class U(lambda)
Caspian Journal of Mathematical Sciences
دوره 11، شماره 2، 2022، صفحه 410-416 اصل مقاله (315.39 K)
نوع مقاله: Research Articles
شناسه دیجیتال (DOI): 10.22080/cjms.2022.3794
نویسندگان
Milutin Obradovic¹؛ Nikola Tuneski^* ²
¹Department of Mathematics, Faculty of Civil Engineering, University of Belgrade, Bulevar Kralja Aleksandra 73, 11000, Belgrade, Serbia
²Department of Mathematics and Informatics, Faculty of Mechanical Engineering, Ss. Cyril and Methodius University in Skopje, Karpos II b.b., 1000 Skopje, Republic of North Macedonia
تاریخ دریافت: 28 آذر 1399، تاریخ پذیرش: 20 مرداد 1401
چکیده
Let $f$ be function that is analytic in the unit disk $D=\{z:\|z\|<1\}$, normalized such that $f(0)=f'(0)-1=0$, i.e., of type $f(z)=z+\sum_{n=2}^{\infty} a_n z^n$. If additionally, \[ \left\| \left(\frac{z}{f(z)}\right)^2 f'(z) -1\right\|<\lambda \quad\quad (z\in D), \] then $f$ belongs to the class $U(\lambda)$, $0<\lambda\le1$. In this paper we prove sharp upper bound of the modulus of the fifth coefficient of $f$ from $U(\lambda)$ in the case when $0.400436\ldots \le\lambda\le1$.
کلیدواژه‌ها
Univalent functions؛ Class U($\lambda$)؛ Fifth coefficient؛ Sharp estimate

آمار تعداد مشاهده مقاله: 160 تعداد دریافت فایل اصل مقاله: 183

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