G. Murugusundaramoorthy, Saurabh Porwal
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.
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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 the present paper, we investigate connections between various subclasses of harmonic univalent functions by using a convolution operator involving the Pascal distribution series.
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.
Let $\mathcal{S}$ denote the family of all functions that are analytic and univalent in the unit disk $\mathbb{D}:=\{z: |z|<1\}$ and satisfy $f(0)=f^{\prime}(0)-1=0$. In the present paper, we consider certain subclasses of univalent functions associated with the exponential function, and obtain the sharp upper bounds on the initial coefficients and the difference of initial successive coefficients for functions belonging to these classes.
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.
Univalent Functions involving Generalized Hypergeometric Series
本文研究广义超几何级数与开单位圆盘内具有正泰勒系数的正规化解析函数子类之间的关联，建立两者间的相互联系。
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 $\mathbb{D} =\{z:\, |z|<1\}$.
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.
In the present paper, we define a new general subclass of bi-univalent functions involving a differential operator in the open unit disk U. For this purpose, we use the Faber polynomial expansions. Several connections to some of the earlier known results are also pointed out.
In this study, a subclass of an univalent function with negative coefficients which is defined by a new general Linear operator have been introduced. The sharp results for coefficients estimators, distortion and closure bounds, Hadamard product, and Neighborhood, and this paper deals with the utilizing of many of the results for classical hypergeometric function, where there can be generalized to m-hypergeometric functions. A subclasses of univalent functions are presented, and it has involving operator which generalizes many well-known. Denote A the class of functions f and we have other resu…
Recently, in their pioneering work on the subject of bi-univalent functions, Srivastava et al. \cite{HMS-AKM-PG} actually revived the study of the coefficient problems involving bi-univalent functions. Inspired by the pioneering work of Srivastava et al. \cite{HMS-AKM-PG}, there has been triggering interest to study the coefficient problems for the different subclasses of bi-univalent functions. Motivated largely by Ali et al. \cite{Ali-Ravi-Ma-Mina-class}, Srivastava et al. \cite{HMS-AKM-PG} and Güney et al. \cite{HOG-GMS-JS-Fib-2018} in this paper, we consider certain classes of bi-univalent…
Bohr Phenomenon for $K$-quasiconformal Harmonic Mappings Involving One Parameter
本文研究$K$-拟共形调和映射的Bohr型不等式，涉及参数或凸组合，并推广至凹单叶函数类，推广了已有结果。
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…
Towards a general distortion theory for univalent functions: Teichmuller spaces and coefficient problems of complex analysis
本文综述作者利用Teichmüller空间深层特征提出的新方法及其在单叶函数系数泛函估计中的成果，并给出推广经典系数猜想的新结果与开放问题。
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 the present paper, we derive the third-order differential subordination and superordination results for some analytic univalent functions defined in the unit disc. These results are associated with generalized Struve functions and are obtained by considering suitable classes of admissible functions. As a consequence, the dual problems which yield the sandwich type relations are presented.
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.
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.
Differential subordination and superordination preserving properties for univalent functions in the open unit disk with an operator involving generalized Bessel functions are derived. Some particular cases involving trigonometric functions of our main results are also pointed out.
In this paper, we introduce and investigate a new subclass of the function class $Σ$ of bi-univalent functions defined in the open unit disk, which are associated with the Hurwitz-Lerch zeta function, satisfying quasi-subordinate conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients $|a_2|$ and $|a_3|$ for functions in this new subclass. Several (known or new) consequences of the results are also pointed out.
In this article, by making use of the linear operator introduced and studied by Srivastava and Attiya \cite{srivastava1}, suitable classes of admissible functions are investigated and the dual properties of the third-order differential subordinations are presented. As a consequence, various sandwich-type theorems are established for a class of univalent analytic functions involving the celebrated Srivastava-Attiya transform. Relevant connections of the new results are pointed out.
In this paper our aim is to extend and improve the sufficient conditions for integral operators involving the normalized forms of the generalized Bessel functions of the first kind to be univalent in the open unit disk as investigated recently by (Erhan, E. Orhan, H. and Srivastava, H. (2011). Some sufficient conditions for univalence of certain families of integral operators involving generalized Bessel functions. Taiwanese Journal of Mathematics, 15 (2), pp.883-917) and (Baricz, Á. and Frasin, B. (2010). Univalence of integral operators involving Bessel functions. Applied Mathematics Letters…
Geometric subfamily of functions convex in some direction and Blaschke products
本文研究满足特定规范化与曲率条件的局部单叶解析函数族，证明其具有涉及 Blaschke 乘积、Schwarz 导数及单叶调和映射的若干优雅性质。
In this article, we establish the Bohr inequalities for the sense-preserving $K$-quasiconformal harmonic mappings defined in the unit disk $\mathbb{D}$ involving classes of Ma-Minda starlike and convex univalent functions, usually denoted by $\mathcal{S}^*(ψ)$ and $\mathcal{C}(ψ)$ respectively, and for $\log (f(z)/z)$ where $f$ belongs to the Ma-Minda classes or satisfies certain differential subordination. We also estimate Logarithmic coefficient's bounds for the functions in $\mathcal{C}(ψ)$ for the case $ψ(\mathbb{D})$ be convex.
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.
Sharp Bohr and Bohr-Rogosinski inequalities involving area measure for close-to-convex harmonic mappings
本文针对近凸调和映射子类，通过引入与面积积分相关的单调函数，建立了用欧几里得距离表示的尖锐Bohr型不等式及含模幂的Bohr-Rogosinski型不等式，并证明半径尖锐性及识别极值函数，推广统一了多个经典结果。
In this article, we impose a new class of fractional analytic functions in the open unit disk. By considering this class, we define a fractional operator, which is generalized Salagean and Ruscheweyh differential operators. Moreover, by means of this operator, we introduce an interesting subclass of functions which are analytic and univalent. Furthermore, this effort covers coefficient bounds, distortions theorem, radii of starlikeness, convexity, bounded turning, extreme points and integral means inequalities of functions belongs to this class. Finally, applications involving certain fraction…
In the past several subclasses of starlike functions are defined involving real part and modulus of certain expressions of functions under study, combined by way of an inequality. In the similar fashion, we introduce a new class $\mathcal{S}^*_{q}(α)$, consisting of normalized analytic univalent functions $f$ in the open unit disk $\mathbb{D}$, satisfying $$\RE\left(\dfrac{z f'(z)}{f(z)}\right) \geq \left|1+\dfrac{z f''(z)}{f'(z)} -\dfrac{z f'(z)}{f(z)}-α\right| \quad (0 \leq α<1).$$ Evidently, $\mathcal{S}^*_{q}(α) \subset \mathcal{S}^*$, the class of starlike functions. We first establish $\…
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