Let $p$ be an analytic function defined on the open unit disc $mathbb{D}$ with $p(0)=1.$ The conditions on $alpha$ and $beta$ are derived for $p(z)$ to be subordinate to $1+4z/3+2z^{2}/3=:varphi_{C}(z)$ when $(1-alpha)p(z)+alpha p^{2}(z)+beta zp'(z)/p(z)$ is subordinate to $e^{z}$. Similar problems were investigated for $p(z)$ to lie in a region bounded by lemniscate of Bernoulli $|w^{2}-1|=1$ ...

‎In this paper we characterize Bergman spaces with‎ ‎respect to double integral of the functions $|f(z)‎ ‎-f(w)|/|z-w|$,‎ ‎$|f(z)‎ -‎f(w)|/rho(z,w)$ and $|f(z)‎ ‎-f(w)|/beta(z,w)$,‎ ‎where $rho$ and $beta$ are the pseudo-hyperbolic and hyperbolic metrics‎. ‎We prove some necessary and sufficient conditions that implies a function to be...

Baker (2019), Barany and Kaenmaki (2019) independently showed that there exist iterated function systems without exact overlaps are super-exponentially close cylinders at all small levels. We adapt the method of obtain further examples this type. prove for any algebraic number \(\beta\ge 2\) real numbers \(s, t\) such system \(\left \{\frac{x}{\beta}, \frac{x+1}{\beta}, \frac{x+s}{\beta}, \fr...

Let $E$ be the self-similar set generated by {\it iterated function system} {\[ f_0(x)=\frac{x}{\beta},\quad f_1(x)=\frac{x+1}{\beta}, \quad f_{\beta+1}=\frac{x+\beta+1}{\beta} \]}with $\beta\ge 3$. {Then} is a with complete {overlaps}, i.e., $f_{0}\circ f_{\beta+1}=f_{1}\circ f_1$, but not totally self-similar. We investigate all its generating systems, give spectrum of $E$, and determine Haus...

Introduction: The central-governor model explains the mechanism of endurance exercise-induced central fatigue, but high-intensity exercise-induced central fatigue has not been investigated yet. This study aimed to research how central fatigue during high-intensity intermittent pedaling alters the neural response, which results in electroencephalography (EEG) recordings. Methods: We assessed ne...