scholarly journals Hankel Determinant for -Valent Alpha-Convex Functions

Geometry ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Gagandeep Singh ◽  
B. S. Mehrok
Keyword(s):  
Upper Bound ◽  
Convex Functions ◽  
Unit Disc ◽  
Hankel Determinant

The objective of the present paper is to obtain the sharp upper bound of for p-valent α-convex functions of the form in the unit disc .

scholarly journals Study of Second Hankel Determinant for Certain Subclasses of Functions Defined by Al-Oboudi Differential Operator

2020 ◽  
Vol 17 (1(Suppl.)) ◽  
pp. 0353
Author(s):  
K. A. Challab et al.
Keyword(s):  
Differential Operator ◽  
Upper Bound ◽  
Unit Disc ◽  
Hankel Determinant ◽  
Special Cases ◽  
Second Hankel Determinant

The concern of this article is the calculation of an upper bound of second Hankel determinant for the subclasses of functions defined by Al-Oboudi differential operator in the unit disc. To study special cases of the results of this article, we give particular values to the parameters A, B and λ

scholarly journals Hankel determinant for certain class of analytic function defined by generalized derivative operator

2012 ◽  
Vol 43 (3) ◽  
pp. 445-453
Author(s):  
Ma'moun Harayzeh Al-Abbadi ◽  
Maslina Darus
Keyword(s):  
Analytic Function ◽  
Upper Bound ◽  
Unit Disc ◽  
Univalent Functions ◽  
Open Unit ◽  
Hankel Determinant ◽  
Open Unit Disc ◽  
Derivative Operator ◽  
Generalized Derivative ◽  
Generalised Derivatives

The authors in \cite{mam1} have recently introduced a new generalised derivatives operator $ \mu_{\lambda _1 ,\lambda _2 }^{n,m},$ which generalised many well-known operators studied earlier by many different authors. By making use of the generalised derivative operator $\mu_{\lambda_1 ,\lambda _2 }^{n,m}$, the authors derive the class of function denoted by $ \mathcal{H}_{\lambda _1 ,\lambda _2 }^{n,m}$, which contain normalised analytic univalent functions $f$ defined on the open unit disc $U=\left\{{z\,\in\mathbb{C}:\,\left| z \right|\,<\,1} \right\}$ and satisfy \begin{equation*}{\mathop{\rm Re}\nolimits} \left( {\mu _{\lambda _1 ,\lambda _2 }^{n,m} f(z)} \right)^\prime > 0,\,\,\,\,\,\,\,\,\,(z \in U).\end{equation*}This paper focuses on attaining sharp upper bound for the functional $\left| {a_2 a_4 - a_3^2 } \right|$ for functions $f(z)=z+ \sum\limits_{k = 2}^\infty {a_k \,z^k }$ belonging to the class $\mathcal{H}_{\lambda _1 ,\lambda _2 }^{n,m}$.

scholarly journals Upper Bound of the Third Hankel Determinant for a Subclass of Close-to-Convex Functions Associated with the Lemniscate of Bernoulli

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 848
Author(s):  
Hari M. Srivastava ◽  
Qazi Zahoor Ahmad ◽  
Maslina Darus ◽  
Nazar Khan ◽  
Bilal Khan ◽  
...  
Keyword(s):  
Unit Disk ◽  
Upper Bound ◽  
Convex Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Hankel Determinant ◽  
Lemniscate Of Bernoulli ◽  
The Third ◽  
The Right

In this paper, our aim is to define a new subclass of close-to-convex functions in the open unit disk U that are related with the right half of the lemniscate of Bernoulli. For this function class, we obtain the upper bound of the third Hankel determinant. Various other related results are also considered.

scholarly journals Bounds on third Hankel determinant for close-to-convex functions

2015 ◽  
Vol 7 (2) ◽  
pp. 210-219 ◽  
Author(s):  
J. K. Prajapat ◽  
Deepak Bansal ◽  
Alok Singh ◽  
Ambuj K. Mishra
Keyword(s):  
Upper Bound ◽  
Convex Functions ◽  
Hankel Determinant

Abstract In this paper, we have obtained upper bound on third Hankel determinant for the functions belonging to the class of close-to-convex functions.

scholarly journals Second Hankel Determinant for a Certain Subclass of Bi-Close to Convex Functions Defined by Kaplan

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 567
Author(s):  
Stanislawa Kanas ◽  
Pesse V. Sivasankari ◽  
Roy Karthiyayini ◽  
Srikandan Sivasubramanian
Keyword(s):  
Upper Bound ◽  
Convex Functions ◽  
Hankel Determinant ◽  
Second Hankel Determinant ◽  
Upper Bound Estimate

In this paper, we consider the class of strongly bi-close-to-convex functions of order α and bi-close-to-convex functions of order β. We obtain an upper bound estimate for the second Hankel determinant for functions belonging to these classes. The results in this article improve some earlier result obtained for the class of bi-convex functions.

scholarly journals Coefficient Bounds for Some Families of Starlike and Convex Functions of Reciprocal Order

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Muhammad Arif ◽  
Maslina Darus ◽  
Mohsan Raza ◽  
Qaiser Khan
Keyword(s):  
Upper Bound ◽  
Convex Functions ◽  
Hankel Determinant ◽  
Coefficient Estimates ◽  
Coefficient Bounds ◽  
Starlike And Convex Functions

The aim of the present paper is to investigate coefficient estimates, Fekete-Szegő inequality, and upper bound of third Hankel determinant for some families of starlike and convex functions of reciprocal order.

scholarly journals Coefficient inequality for transforms of starlike and convex functions

2015 ◽  
Vol 24 (1) ◽  
pp. 69-75
Author(s):  
D. VAMSHEE KRISHNA ◽  
◽  
B. VENKATESWARLU ◽  
T. RAMREDDY ◽  
◽  
...  
Keyword(s):  
Analytic Function ◽  
Complex Plane ◽  
Upper Bound ◽  
Convex Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc ◽  
Toeplitz Determinants ◽  
Starlike And Convex Functions ◽  
Coefficient Inequality

The objective of this paper is to obtain an upper bound for the second Hankel functional associated with the k th root transform ... normalized analytic function f(z) belonging to starlike and convex functions, defined on the open unit disc in the complex plane, using Toeplitz determinants.

An upper bound to the nonlinear functional for certain subclasses of analytic functions associated with Hankel determinant

2014 ◽  
Vol 07 (02) ◽  
pp. 1350042
Author(s):  
D. Vamshee Krishna ◽  
T. Ramreddy
Keyword(s):  
Upper Bound ◽  
Convex Functions ◽  
Analytic Functions ◽  
Hankel Determinant ◽  
Toeplitz Determinants ◽  
Nonlinear Functional ◽  
Determinant Formula ◽  
Starlike And Convex Functions ◽  
Second Hankel Determinant ◽  
Strongly Starlike

The objective of this paper is to obtain an upper bound to the second Hankel determinant [Formula: see text] for the functions belonging to strongly starlike and convex functions of order α(0 < α ≤ 1). Further, we introduce a subclass of analytic functions and obtain the same coefficient inequality for the functions in this class, using Toeplitz determinants.

scholarly journals LOGARITHMIC COEFFICIENTS OF SOME CLOSE-TO-CONVEX FUNCTIONS

2016 ◽  
Vol 95 (2) ◽  
pp. 228-237 ◽  
Author(s):  
MD FIROZ ALI ◽  
A. VASUDEVARAO
Keyword(s):  
Univalent Function ◽  
Upper Bound ◽  
Convex Functions ◽  
Unit Disc ◽  
Starlike Functions ◽  
Logarithmic Coefficients

The logarithmic coefficients$\unicode[STIX]{x1D6FE}_{n}$of an analytic and univalent function$f$in the unit disc$\mathbb{D}=\{z\in \mathbb{C}:|z|<1\}$with the normalisation$f(0)=0=f^{\prime }(0)-1$are defined by$\log (f(z)/z)=2\sum _{n=1}^{\infty }\unicode[STIX]{x1D6FE}_{n}z^{n}$. In the present paper, we consider close-to-convex functions (with argument 0) with respect to odd starlike functions and determine the sharp upper bound of$|\unicode[STIX]{x1D6FE}_{n}|$,$n=1,2,3$, for such functions $f$.

scholarly journals Third Hankel determinant for starlike and convex functions with respect to symmetric points

2016 ◽  
Vol 70 (1) ◽  
pp. 37 ◽  
Author(s):  
D. Vamshee Krishna ◽  
B. Venkateswarlu ◽  
T. RamReddy
Keyword(s):  
Upper Bound ◽  
Convex Functions ◽  
Hankel Determinant ◽  
Toeplitz Determinants ◽  
Starlike And Convex Functions ◽  
Symmetric Points

The objective of this paper is to obtain best possible upper bound to the \(H_{3}(1)\)  Hankel determinant for starlike and convex functions with respect to symmetric points, using Toeplitz determinants.

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