regular functions f in the half-plane Im z > 0 admitting an asymptotic expansion f(z) = c(1)z + c(2)z(2) + c(3)z(3) + gamma(z)z(3), where c(1) > 0, Im c(2) = 0 and the angular limit angle lim(z -> 0) gamma(z)...
详细信息
regular functions f in the half-plane Im z > 0 admitting an asymptotic expansion f(z) = c(1)z + c(2)z(2) + c(3)z(3) + gamma(z)z(3), where c(1) > 0, Im c(2) = 0 and the angular limit angle lim(z -> 0) gamma(z) = 0, are considered. For various conditions on the function f inequalities for the real part of the Schwarzian derivative S-f(0) = 6(c(3)/c(1) - c(2)(2)/c(1)(2)) are established. These inequalities complement and refine some known versions of Schwarz's lemma. The results obtained are close to the well-known Burns-Krantz rigidity theorem on regular self-maps and its generalizations due to Tauraso, Vlacci and Shoikhet. Bibliography: 16 titles.
There must be only a univalent and analytic function on a simply connected region. It will transform the region into a unit circle. However, it satisfies the condition that the function value at one point equals zero ...
详细信息
There must be only a univalent and analytic function on a simply connected region. It will transform the region into a unit circle. However, it satisfies the condition that the function value at one point equals zero and the derivative of this point is more than zero. The reciprocal of the derivative is called the mapping radius of the function at the point. The mapping radius relevantly changes when the point moves. In fact, the mapping radius in the region is a real valued function. The function is continuous and reaches the maximum value within the region. If a simply connected region is the convex region with the symmetrical center, then the mapping radius function obtains the maximum at the symmetrical center of the region.
We present an example of a regular opinion function which, as it evolves in accordance with the discrete-time Hegselmann-Krause bounded confidence dynamics, always retains opinions which are separated by more than two...
详细信息
We present an example of a regular opinion function which, as it evolves in accordance with the discrete-time Hegselmann-Krause bounded confidence dynamics, always retains opinions which are separated by more than two. This confirms a conjecture of Blondel, Hendrickx and Tsitsiklis.
Abstract: Let $\mathfrak {F}_\alpha ^\lambda$ be the class of functions $f(z) = z + {a_2}{z^2} + \cdots$ which are regular in $E = \{ z/|z| < 1\}$ and satisfy \[ \operatorname {Re} \{ {e^{i\alpha }}(1 +...
详细信息
Abstract: Let $\mathfrak {F}_\alpha ^\lambda$ be the class of functions $f(z) = z + {a_2}{z^2} + \cdots$ which are regular in $E = \{ z/|z| < 1\}$ and satisfy \[ \operatorname {Re} \{ {e^{i\alpha }}(1 + zf''(z)/f’(z))\} > \lambda \cos \alpha \] for some $\alpha ,|\alpha | < \pi /2$, and for some $\lambda ,0 \leq \lambda < 1$. The author finds a range on $\alpha$ for which $f(z)$ in $\mathfrak {F}_\alpha ^\lambda$ is univalent in $E$. In particular, the author improves upon the range on a for which $f(z) \in \mathfrak {F}_\alpha ^0$ is known to be univalent in $E$. Also a corresponding result is obtained for those functions $f(z)$ in $\mathfrak {F}_\alpha ^\lambda$ for which $f''(0) = 0$.
We discuss the octonionic regular functions and the octonionic regular operator on the octonionic Heisenberg group. This is the octonionic version of CR function theory in the theory of several complex variables and r...
详细信息
We discuss the octonionic regular functions and the octonionic regular operator on the octonionic Heisenberg group. This is the octonionic version of CR function theory in the theory of several complex variables and regular function theory on the quaternionic Heisenberg group. By identifying the octonionic algebra with , we can write the octonionic regular operator and the associated Laplacian operator as real -matrix differential operators. Then we use the group Fourier transform on the octonionic Heisenberg group to analyze the associated Laplacian operator and to construct its kernel. This kernel is exactly the Szego kernel of the orthonormal projection from the space of functions to the space of regular functions on the octonionic Heisenberg group.
暂无评论