On some $n$-starlike integral operators
K. O. Babalola
通过对Babalola和Opoola \cite{KT}引理的完善，证明了某些广义积分算子在开单位圆盘$E=\{z\in \mathbb{C}: |z|<1\}$中保持$n$ -星形性.我们的结果推广和改进了许多已知的结果。
By a completion of a lemma of Babalola and Opoola \cite{KT}, we prove that certain generalized integral operators preserve $n$-starlikeness in the open unit disk $E=\{z\in \mathbb{C}: |z|<1\}$. Our results generalize, extend and improve many known ones.
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In this paper, we shall find the order of starlikeness and convexity for integral operators \begin{equation*} \mathbb{F}_{α_{j},β_{j},λ_{j},ζ}(z)=\left\{ ζ\int\limits_{0}^{z}t^{ζ-1}\prod_{j=1}^{n}\left( \frac{\mathbb{E} _{α_{j},β_{j}}(t)}{t}\right) ^{1/λ_{j}}dt\right\} ^{1/ζ}, \end{equation*} where the functions $\mathbb{E}_{α_{j},β_{j}}$ are the normalized Mittag-Leffler functions.
On some starlike mappings involving certain convolution operators
本文通过某些卷积算子引入了一类新的单叶星形映象，对单位圆盘上的单叶星形映象族作了一些贡献。给出了一个新的单叶性条件，并举例说明。文中还给出了新子类函数的一些基本特征。
Order of Starlikeness and Convexity of certain integral transforms using duality techniques
对于$α\geq 0$、$β<1$和$γ\geq 0$，考虑满足条件\begin{align*} {\rm Re\,} \left( e^{iϕ}\left((1-α+2γ)f/z+(α-2γ)f'+ γzf''-β\right)\frac{}{}\right)>0, \quad ϕ\in {\mathbb{R}},{\,}z\in {\mathbb{D}}; \end{align*}的类$\mathcal{W}_β(α,γ)$。$ξ$的Pascu类--$σ$阶凸函数$(M(σ,{\,}ξ))$，具有解析特征\begin{align*} {\rm Re\,}\frac{ξz(zf'(z))'+(1-ξ)zf'(z)}{ξzf'(z)+(1-ξ)f(z)}>σ,\quad 0\leq σ< 1,\quad z\in {\mathbb{D}}, \end{align*}统一了$σ$阶星形函数类和凸函数类，研究了$λ(t)$的容许条件和充分条件，使得积分变换\begin{align*} V_λ(f)(z)= \int_0^1 λ(t) \frac{f(tz)}{t} dt, \end{align*}将函数从$\mathcal{W}_β(α,γ)$映射到$M(σ,{\,}ξ)$ .进一步讨论了与经典积分变换有关的$λ(t)$的几个有趣的应用。
The theory of $q$-analogs frequently occurs in a number of areas, including the fractals and dynamical systems. The $q$-derivatives and $q$-integrals play a prominent role in the study of $q$-deformed quantum mechanical simple harmonic oscillator. In this paper, we define a symmetric $q$-derivative operator and study new family of univalent functions defined by use of that operator. We establish some new relations between functions satisfying analytic conditions related to conical sections.
Functional inequalities for starlike and convex functions associated with $g$-derivative operator
研究与g-导数算子相关的星形和凸函数，通过引入新算子定义新函数类，并利用解析函数从属原理进行系数估计，得出Fekete-Szegö不等式、Toeplitz行列式和Hankel行列式的界。
For an analytic function $f$ defined on the unit disk $|z|<1$, let $Δ(r,f)$ denote the area of the image of the subdisk $|z|<r$ under $f$, where $0<r\le 1$. In 1990, Yamashita conjectured that $Δ(r,z/f)\le πr^2$ for convex functions $f$ and it was finally settled in 2013 by Obradović and et. al.. In this paper, we consider a class of analytic functions in the unit disk satisfying the subordination relation $zf'(z)/f(z)\prec (1+(1-2β)αz)/(1-αz)$ for $0\le β<1$ and $0<α\le 1$. We prove Yamashita's conjecture problem for functions in this class, which solves a partial solution to an open problem …
For $α\geq 0$, $δ>0$, $β<1$ and $γ\geq 0$, the class $\mathcal{W}_β^δ(α,γ)$ consist of analytic and normalized functions $f$ along with the condition \begin{align*} {\rm Re\,} e^{iϕ}(\dfrac{}{}(1\!-\!α\!+\!2γ)\!({f}/{z})^δ+(α\!-\!3γ\!+\!γ[\dfrac{}{}(1-{1}/δ)({zf'}/{f})+ {1}/δ(1+{zf''}/{f'})]).\\ .\dfrac{}{}({f}/{z})^δ\!({zf'}/{f})-β)>0, \end{align*} where $ϕ\in\mathbb{R}$ and $|z|<1$, is taken into consideration. The class $\mathcal{S}^\ast_s(ζ)$ be the subclass of the univalent functions, defined by the analytic characterization ${\rm Re}{\,}({zf'}/{f})>ζ$, for $0\leq ζ< 1$, $0<δ\leq\frac{1}{…
In this paper, we considered a generalized class of starlike functions defined by Kanas and Răducanu\cite{10} to obtain integral means inequalities and subordination results. Further, we obtain the for various subclasses of starlike functions.
In the present paper, we study a new subclass $\mathcal{M}_p(α,β)$ of $p$--valent functions and obtain some inequalities concerning the coefficients for the desired class. Also, by use of the Hadamard product, we define a general operator and find a condition such that it belongs to the class $\mathcal{M}_p(α,β)$.
Let $f$ and $g$ be analytic functions on the open unit disk of the complex plane with $f/g$ belonging to the class $\mathcal{P} $ of functions with positive real part consisting of functions $p$ with $p(0)=1$ and $\operatorname{Re} p(z)>0$ or to its subclass consisting of functions $p$ with $|p(z)-1|<1$. We obtain the sharp radius constants for the function $f$ to be starlike of order $α$, parabolic starlike, etc. when $g/k\in\mathcal{P}$ where $k$ denotes the Koebe function defined by $k(z)=z/(1-z)^2$.
The error function occurs widely in multiple areas of mathematics, mathematical physics and natural sciences. There has been no work in this area for the past four decades. In this article, we estimate the coefficient bounds with q-difference operator for certain classes of the spirallike starlike and convex error function associated with convolution product using subordination as well as quasi-subordination. Though this concept is an untrodden path in the field of complex function theory, it will prove to be an encouraging future study for researchers on error function.
In this paper, we prove necessary and sufficient conditions for a sense-preserving harmonic function to be absolutely convex in the open unit disk. We also estimate the coefficient bound and obtain growth, covering and area theorems for absolutely convex harmonic mappings. A natural generalization of the classical Bernardi type operator for harmonic functions is considered and its connection between certain classes of uniformly starlike harmonic functions and uniformly convex harmonic functions is also investigated. At the end, as applications, we present a number of results connected with hyp…
On the Convexity of the Bernardi Integral Operator
该研究证明Bernardi积分算子可将特定有界星形函数类映射为凸函数类，改进了已有结果，并提出通用统一方法以研究其他多种保留单叶、p叶函数子类性质的积分算子。
Sharp Coefficient Bounds for certain $q$-Starlike Functions
本文引入与Ma-Minda函数相关的$q$-星形函数子类，系统建立了Fekete-Szegö、Hankel和Toeplitz行列式的尖锐系数估计，并通过新积分表示证明$q$-系数估计的尖锐性。
In this paper, we study subclass of analytic function with negative coefficient defined by integral operator in the unit disc $U = \left\{ {z \in C:\left| z \right| < 1} \right\}$. The results are included coefficient estimates, closure theorem and distortion theorems of functions belonging to this subclass. Also, we presented detailed study of uniformly convex and uniformly starlike functions.
Controlled approximation and interpolation for some classes of holomorphic functions
本文给出了单位圆盘上三类密切相关的全纯函数的构造逼近方法：星形和螺形函数类、半群生成元类和具有正实部的函数类。星状函数或螺状函数可以定义为奇异微分方程的解，而这些奇异微分方程在内部奇点向边界运动时一般是不稳定的。同时，可以建立一个摄动公式，它将关于边界点的星形（或螺旋形）函数连续变换为关于内点的星形（或螺旋形）函数。这个公式是基于确定上述微分方程的全纯生成元的适当近似方法。反过来，著名的Berkson-Porta参数表示的全纯生成元引导我们研究一类函数的逼近插值问题的正实部。虽然这个问题是独立的利益，我们在这里提出的解决方案是再次根据Berkson-Porta公式。最后，我们应用这些结果解决了单参数全纯自映射半群的自然扰动问题，以及复合算子半群的本征值问题。
In this paper, we define a new subclass of $k$-uniformly starlike functions of order $γ,\ (0\leqγ<1)$ by using certain generalized $q$-integral operator. We explore geometric interpretation of the functions in this class by connecting it with conic domains. We also investigate $q$-sufficient coefficient condition, $q$-Fekete-Szegö inequalities, $q$-Bieberbach-De Branges type coefficient estimates and radius problem for functions in this class. We conclude this paper by introducing an analogous subclass of $k$-uniformly convex functions of order $γ$ by using the generalized $q$-integral operato…
Certain Subclass of Harmonic Multivalent Functions Defined by New Linear Operator
该研究在穿孔开圆盘内构造新算子，提出一类带正系数的亚纯函数新子类，并推导其系数估计、偏差定理等多项几何性质，丰富了调和多叶函数领域的研究内容。
The conditions on $A$, $B$, $β$ and $γ$ are obtained for an analytic function $p$ defined on the open unit disc $\mathbb{D}$ and normalized by $p(0)=1$ to be subordinate to $(1+Az)/(1+Bz)$, $-1\leq B<A \leq 1$ when $p(z)+ zp'(z)/(βp(z)+γ)$ is subordinate to $e^{z}$. The conditions on these parameters are derived for the function $p$ to be subordinate to $\sqrt{1+z}$ or $e^{z}$ when $p(z)+ zp'(z)/(βp(z)+γ)$ is subordinate to $(1+Az)/(1+Bz)$. The conditions on $β$ and $γ$ are determined for the function $p$ to be subordinate to $e^{z}$ when $p(z)+ zp'(z)/(βp(z)+γ)$ is subordinate to $\sqrt{1+z}$…
In this paper, by making use of a certain family of fractional derivative operators in the complex domain, we introduce and investigate a new subclass $\mathcal{P}_{τ,μ}(k,δ,γ)$ of analytic and univalent functions in the open unit disk $\mathbb{U}$. In particular, for functions in the class $\mathcal{P}_{τ,μ}(k,δ,γ)$, we derive sufficient coefficient inequalities, distortion theorems involving the above-mentioned fractional derivative operators, and the radii of starlikeness and convexity. In addition, some applications of functions in the class $\mathcal{P}_{τ,μ}(k,δ,γ)$ are also pointed out.
Integral operators on analytic Morrey spaces
本文研究了积分算子$I_{g}$和$T_{g}$在解析Morrey空间上的有界性.进一步给出了这些算子的范数和本质范数。
On a particular integral operator
我们考虑一个积分算子$\mathcal{I}$，其特殊情况下，在各种情况下进行了研究。使用适当的变换，我们把这个算子写成加权复合算子。然后，我们给出了加权Dirichlet空间上的有界性准则，并应用这个结果证明了某些积分算子在加权Dirichlet空间上是有界的，统一了这一方法，推广了以前的结果.
On the scaling limit of a singular integral operator
利用单值问题的差分方程方法，导出了奇异积分算子的标度极限和Schauder界.
In this article, we determine sharp Bohr-type radii for certain complex integral operators defined on a set of bounded analytic functions in the unit disk.
Product of Volterra type integral and composition operators on weighted Fock spaces
我们刻画了作用于加权Fock空间之间的Volterra型积分算子和复合算子的有界、紧和Schatten类乘积。我们的结果表示为复平面$\CC$上的某些Berezin型积分变换。我们还利用积分变换估计了这些算子的范数和本质范数。我们的所有结果是有效的加权复合算子之间的一类加权Fock空间考虑。
Integral-type operators from Hardy space to Bloch space on the upper half-plane
刻画了从Hardy空间到Bloch空间的积分型算子的紧性在上半平面$Π_+=\{z\in\mathbb{C}:Imz>0\}$上的有界性.
The main purpose of this paper is to derive some subordination and superordination results involving certain of integral operator for meromorphic univalent functions in the punctured open unit disk. Several sandwich-type results are also obtained.
In this article, we study the Bohr type inequality for {C}esáro operator and {B}ernardi integral operator acting on the space of analytic functions defined on a simply connected domain containing the unit disk $\mathbb{D}$.
We survey recent work and announce new results concerning two singular integral operators whose kernels are holomorphic functions of the output variable, specifically the Cauchy-Leray integral and the Cauchy-Szeg\H o projection associated to various classes of bounded domains in $\mathbb C^n$ with $n\geq 2$.
We study the boundedness and compactness of the generalized Volterra integral operator on weighted Bergman spaces with doubling weights on the unit disk. A generalized Toeplitz operator is defined and the boundedness, compactness and Schatten class of this operator are investigated on the Hilbert weighted Bergman space. As an application, Schatten class membership of generalized Volterra integral operators are also characterized. Finally, we also get the characterizations of Schatten class membership of generalized Toeplitz operator and generalized Volterra integral operators on the Hardy spac…
Integral operators induced by the Fock kernel
研究了$C^n$上Fock空间的再生核诱导的一类积分算子的$L^p$有界性，得到了其范数.
We study the topological structure of the space of Volterra-type integral operators on Fock spaces endowed with the operator norm. We proved that the space has the same connected and path connected components which is the set of all compact operators acting on the Fock spaces. We also obtained a characterization of isolated points of the space of the operators and showed that there exists no essentially isolated Volterra-type integral operator.
We study some mapping properties of Volterra type integral operators and composition operators on model spaces. We also discuss and give out a couple of interesting open problems in model spaces where any possible solution of the problems can be used to study a number of other operator theoretic related problems in the spaces.
On asymptotic and essential Toeplitz and Hankel integral operator
该文研究希尔伯特空间$H^2$上的广义积分算子，刻画其为不同类型渐近Toeplitz、Hankel算子的条件，并给出对应本质算子的符号刻画。
We study Schatten--von Neumann properties of multiple operator integrals with integrands in the Haagerup tensor product of $L^\infty$ spaces. We obtain sharp, best possible estimates. This allowed us to obtain sharp Schatten--von Neumann estimates in the case of {\it Haagerup-like} tensor products.
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