K. O. Babalola
This paper makes a modest contribution to the family of starlike univalent mappings in the open unit disk, by the introduction of some new subclasses of them via certain convolution operators. A new univalence condition is given with examples. Some basic characterizations of functions of the new subclasses are also mentioned.
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We investigate the univalency and the directional convexity of the convolution $ϕ\tilde{*}f=ϕ*h+\overline{ϕ*g}$ of the harmonic mapping $f=h+\bar{g}$ with a mapping $ϕ$ whose convolution with the mapping $z+\sum_{k=2}^{\infty}k^nz^k$ is starlike (and such a mapping $ϕ$ is called $n$-starlike). In addition, we investigate the directional convexity of (i) the convolution of an analytic convex mapping with the slanted half-plane mapping, and (ii) the partial sums of the convolution of a $6$-starlike mapping with the harmonic Koebe mapping and the harmonic half-plane mapping.
In the present paper, we discuss several basic properties of a class of quasiconformal close-to-convex harmonic mappings with starlike analytic part, such results as coefficient inequalities, an integral representation, a growth theorem, an area theorem, and radii of close-to-convexity of partial sums of the class, are derived.
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.
In the present paper two certain subclasses of the starlike functions associated with the vertical strip are considered. The main aim of this paper is to investigate some basic properties of these classes such as, subordination relations, sharp inequalities for sums involving logarithmic coefficients and estimate of logarithmic coefficients.
Let $\mathcal{A}_n$ be the class of analytic functions $f(z)$ of the form $f(z)=z+\sum_{k=n+1}^\infty a_kz^k,n\in\mathbb{N}$ and let \begin{align*} Ω_n:=\left\{f\in\mathcal{A}_n:\left|zf'(z)-f(z)\right|<\frac{1}{2},\; z\in\mathbb{D}\right\}. \end{align*} We make use of differential subordination technique to obtain sufficient conditions for the class $Ω_n$, and then employ these conditions to construct functions which involve double integrals and members of $Ω_n$. We also consider a subclass $\widehatΩ_n\subsetΩ_n$ and obtain subordination results for members of $\widehatΩ_n$ besides a necessa…
Coefficient estimates for the class of q-starlike functions
本文利用卷积定义了 $q$-星象函数类，通过 Carathéodory-Toeplitz 定理和 Parseval 定理，分别推导了实数和复数 $q$ 下其 Taylor 系数及行列式的精确上界。
The hereditary property of convexity and starlikeness for conformal mappings does not generalize to univalent harmonic mappings. This failure leads us to the notion of fully starlike and convex mappings of order α, (0\leq α<1). A bound for the radius of fully starlikeness and fully convexity of order αis determined for certain families of univalent harmonic mappings. Convexity is not preserved under the convolution of univalent harmonic convex mappings, unlike in the analytic case. Given two univalent harmonic convex mappings f and g, the problem of finding the radius r_{0} such that f*g is a …
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.
We extend our definition (in a recent paper \cite{KB}) of the coefficient determinants of analytic mappings of the unit disk to include many Fekete-Szeg$\ddot{o}$-type parameters, and compute the best possible bounds on certain specific determinants for the choice class of starlike functions.
In this paper, we obtain coefficient criteria for a normalized harmonic function defined in the unit disk to be close-to-convex and fully starlike, respectively. Using these coefficient conditions, we present different classes of harmonic close-to-convex (resp. fully starlike) functions involving Gaussian hypergeometric functions. In addition, we present a convolution characterization for a class of univalent harmonic functions discussed recently by Mocanu, and later by Bshouty and Lyzzaik in 2010. Our approach provide examples of harmonic polynomials that are close-to-convex and starlike, res…
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。
Toeplitz determinants for starlike mappings of order α in several complex variables
该研究针对多复变量中α级星型映射，建立了涉及弗雷歇导数的两个托普利茨行列式的精确界，明确极值映射并验证了估计的精确性。
The main object of the present paper is to, introduce the. class of meromorphic univalent functions Involving! hypergeomatrc function .We obtain~ some interesting geometric properties according to coefficient inequality , growth and distortion theorems , radii of starlikeness and convexity for the" functions in our subclass.
In this paper, we introduce and investigate a novel class of analytic and univalent functions of negative coefficients in the open unit disk. For this function class, we obtain characterization and distortion theorems as well as the radii of close-to-convexity, starlikeness and convexity by using fractional calculus techniques.
Certain geometric properties of planar harmonic mapping involving four parameter Wright functions
本文构造了与四参数Wright函数相关的调和映射，建立了其满足调和星形性和凸性的充分条件，并研究了调和近凸映射子类间的关系，所得结果新颖且具有意义。
In this paper, we prove various radius results and obtain sufficient conditions using the convolution for the Ma-Minda classes $\mathcal{S}^*(ψ)$ and $\mathcal{C}(ψ)$ of starlike and convex analytic functions. We also obtain the Bohr radius for the class $ S_{f}(ψ):= \{g(z)=\sum_{k=1}^{\infty}b_k z^k : g \prec f \}$ of subordinants, where $f\in \mathcal{S}^*(ψ).$ The results are improvements and generalizations of several well known results.
Radius of convexity of certain classes of functions defined by convolution
研究由卷积定义的凹函数类与星形函数类的凸半径，利用卷积技巧得到凸半径的下界。
We establish the membership criteria in terms of Hadamard product for a normalized analytic function to be in the class of infinitesimal generators. Furthermore, the embedding of various subclasses of normalized univalent functions in the class of infinitesimal generators and the radii problems for this class are studied. The results derived, generalize the already known results.
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.
Let $E$ be the open unit disk $\{z\in \mathbb{C}: |z|<1\}$. Let $A$ be the class of analytic functions in $E$, which have the form $f(z)=z+a_2z^2+...$. We define operators $L_n^σ\colon A\to A$ using the convolution *. Using these operators, we define and study new classes of functions in the unit disk. Moreover, we obtain some basic properties of the new classes, namely inclusion, growth, covering, distortion, closure under certain integral transformation and coefficient inequalities.
Let f_β= h_β+\bar{g}_βand F_a = H_a +\bar{G}_a be harmonic mappings obtained by shearing of analytic mappings h_β+g_β= 1/(2i\sinβ)log((1 + ze^{iβ})/(1 + ze^{-iβ})), 0<β<πand H_a+G_a = z/(1-z), respectively. Kumar et al. [5] conjectured that if ω(z)=e^{iθ}z^n (θ\in R, n\in N) and ω_a(z)=(a-z)/(1-az), a\in(-1,1) are dilatations of f_βand F_a, respectively, then F_a\ast f_β\in S_H^0 and is convex in the direction of the real axis provided a\in[(n-2)/(n + 2), 1).They claimed to have verified the result for n = 1, 2, 3 and 4 only. In the present paper, we settle the above conjecture in the affirmat…
In the present paper, we investigate connections between various subclasses of harmonic univalent functions by using a convolution operator involving the Pascal distribution series.
The purpose of the present paper is to establish connections between various subclasses of analytic univalent functions by applying certain convolution operator involving Touchard polynomials. To be more precise, we investigate such connections with the classes of analytic univalent functions with positive coefficients in the open unit disk U.
In this paper our purpose is to find upper bound estimate for the second Hankel determinant $|a_{2}a_{4}-a_{3}^{2}|$ for functions defined by convolution belonging to the class $\mathcal{N}_σ^{μ,δ}(λ,t)$ by using Chebyshev polynomials.
We consider the integral operator $\mathcal{I}^{a,b,c}_{d,e}(f)(z)$ involving Clausen's Hypergeometric Function by means of convolution introduced by Chandrasekran and Prabhakaran for investigation. The conditions on the parameters $ a,b, c$ are determined using the integral operator $\mathcal{I}^{a,\frac{b}{2},\frac{b+1}{2}}_{\frac{c}{2}, \frac{c+1}{2}}(f)(z)$ to study the geometric properties of Clausen's Hypergeometric Function for various subclasses of univalent functions.
In this work, we derived the necessary and sufficient conditions on parameters for $_3F_2(^{a,b,c}_{b+1,c+1};z)$ Hypergeometric Function to be in the classes $\mathcal{M}^{\ast}(λ,α)$ and $\mathcal{N}^{\ast}(λ,α)$ and information regarding the image of function $_3F_2(^{a,b,c}_{b+1,c+1};z)$ belonging to $\mathcal{R}^τ(A,B)$ by applying the convolution operator in open unit disc $\mathbb{D} =\{z:\, |z|<1\}$.
Integral representation and functional inequalities involving generalized polylogarithm
本文用Dirichlet级数与Laplace表示及Hadamard卷积两种方法，得到广义多对数函数的单、双积分表示，并证明其完全单调性、Turan不等式、凸性与界，另给出Lerch超越函数积分表示及Hadamard卷积的替代证明。
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