Zobrazeno 1 - 10
of 223
pro vyhledávání: '"Ali, Rosihan M."'
The function $G_\alpha(z)=1+ z/(1-\alpha z^2)$, \, $0\leq \alpha <1$, maps the open unit disc $\mathbb{D}$ onto the interior of a domain known as the Booth lemniscate. Associated with this function $G_\alpha$ is the recently introduced class $\mathca
Externí odkaz:
http://arxiv.org/abs/2201.01042
Let $h$ be a non-vanishing analytic function in the open unit disc with $h(0)=1$. Consider the class consisting of normalized analytic functions $f$ whose ratios $f(z)/g(z)$, $g(z)/z p(z)$, and $p(z)$ are each subordinate to $h$ for some analytic fun
Externí odkaz:
http://arxiv.org/abs/2101.01617
For $f(z) = \sum_{n=0}^{\infty} a_n z^n$ and a fixed $z$ in the unit disk, $|z| = r,$ the Bohr operator $\mathcal{M}_r$ is given by \[\mathcal{M}_r (f) = \sum_{n=0}^{\infty} |a_n| |z^n| = \sum_{n=0}^{\infty} |a_n| r^n.\] This papers develops normed t
Externí odkaz:
http://arxiv.org/abs/1912.11787
Let ${\mathcal M}$ be the class of analytic functions in the unit disk $\ID$ with the normalization $f(0)=f'(0)-1=0$, and satisfying the condition $$\left |z^2\left (\frac{z}{f(z)}\right )''+ f'(z)\left(\frac{z}{f(z)} \right)^{2}-1\right |\leq 1, \qu
Externí odkaz:
http://arxiv.org/abs/1905.01694
Let $f=h+\overline{g}$ be a harmonic univalent map in the unit disk $\mathbb{D}$, where $h $ and $g$ are analytic. We obtain an improved estimate for the second coefficient of $h$. This indeed is the first qualitative improvement after the appearance
Externí odkaz:
http://arxiv.org/abs/1807.05654
This paper treats the class of normalized logharmonic mappings f(z) = zh(z)bar{g(z)} in the unit disk satisfying {\phi}(z) = zh(z)g(z) is analytically typically real. Every such mapping f is shown to be a product of two particular logharmonic mapping
Externí odkaz:
http://arxiv.org/abs/1710.01443
For a fixed $a \in \{1, 2, 3, \ldots\},$ the radius of starlikeness of positive order is obtained for each of the normalized analytic functions \begin{align*} \mathtt{f}_{a, \nu}(z)&:= \bigg(2^{a \nu-a+1} a^{-\frac{a(a\nu-a+1)}{2}} \Gamma(a \nu+1) {}
Externí odkaz:
http://arxiv.org/abs/1707.00379
Publikováno v:
29 pages; Will be published by "Springer International Publishing AG 2016", N.K. Govil et al. (eds.), Progress in Approximation Theory and Applicable Complex Analysis, Springer Optimization and Its Applications 117
The Bohr inequality, first introduced by Harald Bohr in 1914, deals with finding the largest radius $r$, $0
Externí odkaz:
http://arxiv.org/abs/1612.00597
Publikováno v:
Bulletin of the Malaysian Mathematical Sciences Society (2), Volume 34 (2011), No3, pp. 611-629
Functions with fixed initial coefficient have been widely studied. A new methodology is proposed in this paper by making appropriate modifications and improvements to the theory of second-order differential subordination. Several interesting examples
Externí odkaz:
http://arxiv.org/abs/1208.0150
Publikováno v:
Bulletin of the Malaysian Mathematical Sciences Society (2), Vol. 36 (2013), no. 1, 23-38
Radius constants for several classes of analytic functions on the unit disk are obtained. These include the radius of starlikeness of a positive order, radius of parabolic starlikeness, radius of Bernoulli lemniscate starlikeness, and radius of unifo
Externí odkaz:
http://arxiv.org/abs/1207.4529